It seems the answer depends substantially how such a poll question was phrased, and perhaps even when it was asked.
Nuffield College's Centre for Social Investigation conducted a survey some 18 months after the Brexit referendum vote, while the UK Parliamentary showdown over Brexit was happening, which found that
I didn’t want the EU to have any role in UK law-making
was the 2nd ranked choice of those said they voted Leave, after immigration, and it wasn't very far off percentage-wise, although there's only a graph in the summary I found.
Notes: Each bar shows the distribution of Leave voters according to how they ranked the corresponding reason for voting
Leave. Bars are ordered from left to right by the percentage-weighted mean rank. Sample weights were applied.
An important methodological caveat is that the data presented here concern people’s stated reasons for
voting Leave or Remain, assessed more than 18 months after the referendum took place. It is therefore possible
that they do not reflect the true reasons people voted the way they did. For example, they could be biased by the
tendency for people to justify their decisions with post-hoc rationalisations.
When asked to rank the reasons why their counterparts voted the way they did, Leave voters characterise Remain voters more accurately than Remain voters characterise Leave voters. In particular, Remain voters underestimate the importance that Leave voters attach to the EU having no role in UK law-making.
N.B. this was a substantially larger sample than from the paper you found:
Approximately 3,000 respondents were surveyed online by the polling company Kantar between 2nd of February and 8th of March, 2018
Also, the paper mentions other surverys, which depending on the wording of the questions, have produced even more different results, e.g. there's a YouGov survey in which immigration came second, behind a complexly phrased proposition that includes "a better balance between Britain's right to act independently":
YouGov asked Leave and Remain voters to say which reason from a list of eight was the most important when deciding how to vote in the referendum. The most frequently selected reason among Leave voters––ticked by 45%––was, ‘to strike a better balance between Britain's right to act independently, and the appropriate level of co-operation with other countries’. The second most frequently selected reason among Leave voters––ticked by 26%––was, ‘to help us deal better with the issue of immigration’.
[citing:] YouGov. (2016). On the day poll [Sample Size: 4772 UK Adults; Fieldwork: 23rd June 2016]. YouGov, published online.
And another prior poll they mention:
Lord Ashcroft asked Leave voters to rank four possible reasons for voting Leave, and asked Remain voters to rank four possible reasons for voting Remain. The two most important reasons for voting Leave were: ‘The principle that decisions about the UK should be taken in the UK’, which was ranked first by
49% of Leave voters; and ‘A feeling that voting to leave the EU offered the best chance for the UK to regain control over immigration and its own borders’, which was ranked first by 33% of Leave voters.
[citing:] Lord Ashcroft. (2016). How the United Kingdom voted on Thursday… and why. Lord Ashcroft Polls, published online.
And a 3rd prior poll mentioned in this paper:
the British Election Study team asked their respondents an open-ended question just prior to the
referendum, namely ‘What matters most to you when deciding how to vote in the EU referendum?’. They
coded the responses into 54 categories encompassing the key themes that respondents mentioned. The most
frequently cited reasons for voting Leave were ‘Sovereignty/EU bureaucracy’ and ‘Immigration’ (both
mentioned by around 30% of those who said they intended to vote Leave).
[citing:] Prosser, C., Mellon, J. & Green, J. (2016). What mattered most to you when deciding how to vote in the EU referendum? British Election Study, 11 July, published online.
So, it looks like the less directly questions spoke of "regulation" and more generally in terms of [law-]independence from Brussels, the more Leaver voters agreed with the statement, but there's also the issue of when the questions were asked, as they may have been influenced by campaigning messaging, what was the salient issue on the news etc.
I you care about peer review, the same CSI academic is the lead author of such a paper, which is a different in scope, but self-cites the aforementioned study. The latter paper's main thrust is that
argue instead that the UK’s vote to leave stems, at least in part, from
Britons’ comparatively weak sense of European identity.
And using various measures for that they e.g. have a graph like this:
Somewhat reflecting that, an early 2020 YouGov poll commissioned by "Best for Britain" (an org that campaigned pro-Remain) found that few in the UK were in favor of relaxing specific regulations post-Brexit. As I can't find the YouGov poll itself, I'll have to quote the press release of the org that sponsored it:
With reports this week that the EU will demand that Britain retains its ban on chlorinated chicken ahead of negotiations with the US over a trade deal, our poll shows that only one in ten people think Britain should seek to relax food and product safety standards from the current EU-set standards. Half of those who responded said they wanted to maintain current levels of regulation in this area (49%), while over a third thought the rules should be stricter (37%).
On the environment, where the EU fears regulatory divergence could lead to Britain undermining its flagship ‘Green New Deal’ programme, respondents were eager to see higher levels of regulation. While around a third of respondents said they would like standards kept the same (28%), twice as many people thought standards should be made stricter (57%).
Three-quarters of respondents said they thought labour market standards should be kept or made stricter, compared to just 11% who said standards should be relaxed.
The pro-Leave (or at least pro-free-market) camp attacked this poll on how it was worded:
Victoria Hewson of the free-market IEA think-tank said the polling was “misleading”, adding: [...] “If the poll had asked ‘Should the British Government or the EU decide on our laws?’ the answer to their questions may well have been different.
Now that's not to say that specific segments of the UK public didn't take issue with
specific EU regulation areas. For example, there's a paper on the attitudes of Scottish
fishermen, who based on a sample (N = 69) overwhelmingly (93%) voted for Brexit
and had overwhelmingly negative attitudes towards anything EU. Somewhat ironically,
that paper/survey failed to ask the more specific question whether the Common Fisheries
Policy was at the core of this antipathy, but assumed citing a PhD thesis that it is so.