If we take "UK's position" to mean the Political Declaration that accompanies the Withdrawal Agreement (both agreed by May with the EU, but 2-3 times rejected by MPs; the Declaration twice, the Agreement thrice) then this [tentatively] common vision with the EU says:
[23.] The economic partnership should ensure no tariffs, fees, charges or quantitative restrictions
across all sectors, with ambitious customs arrangements that, in line with the Parties'
objectives and principles above, build and improve on the single customs territory provided
for in the Withdrawal Agreement which obviates the need for checks on rules of origin.
[29.] The Parties should conclude ambitious, comprehensive and balanced arrangements on trade in
services and investment in services and non-services sectors, respecting each Party's right to
regulate. The Parties should aim to deliver a level of liberalisation in trade in services well
beyond the Parties’ World Trade Organization (WTO) commitments and building on recent
Union Free Trade Agreements (FTAs).
[30.] In line with Article V of the General Agreement on Trade in Services, the Parties should aim
at substantial sectoral coverage, covering all modes of supply and providing for the absence of
substantially all discrimination in the covered sectors, with exceptions and limitations as
appropriate. The arrangements should therefore cover sectors including professional and
business services, telecommunications services, courier and postal services, distribution
services, environmental services, financial services, transport services and other services of
So they aim for a fairly comprehensive deal in both goods and services. That's perhaps even more ambitious than the deal with Japan or Canada, so call it Canada+ or something like that. Do note that in the jungle of Brexit proposals, the same term has been used to mean something somewhat different
Canada plus plus would mean a hard Brexit and an arms-length relationship with the EU based on reducing tariffs and trade barriers and harmonising regulations. It is attractive to the Brexiters because it would keep Britain out of the single market and customs union. But many Remainers would consider it to be very similar to a no-deal Brexit. It does have the advantage, however, of being supported by the dissenters in the House of Commons – as long as the backstop is not part of the deal.
As one pundit said comparing the multiple Canada+ visions:
Go for Canada-plus
Ardent Brexiters have claimed that May has a simple option. “The PM must go straight back to the EU’s [free-trade agreement] offered by Tusk in March,” said the former cabinet minister Owen Paterson.
This ignores the fact that the EU will only agree a free-trade deal if the UK signs the existing withdrawal agreement, which includes the Irish backstop. When the EU talks of “pluses” in any Canada-style deal, it means other non-trade deals on security, fisheries and foreign policy. When Brexiters talk of pluses, or Supercalifragilisticexpialidocious Canada, they have been looking for advantages that Brussels has repeatedly ruled out.
The take-home message from this is that the future relation can be reached either by upgrading a no-deal or downgrading from May's Withdrawal Agreement. Those who can't stand the backstop (included in the Agreement) want the path former... or they want something completely different in the long, e.g. UK being unilaterally tariff-free with the world etc.
So I'm largely eschewing what "hard brexit"/"no-deal" means in terms of future relations, since it depends on who's talking and what else they envisage should happen after the event. If nothing else happens, a no-deal Brexit just reverts the UK to WTO rules, in terms of trade. Even this is not a simple affair, because the UK is currently [re]negotiating its (future) WTO schedules.
Finally, the vision from the Declaration has been also called "Brexeternity" because its wide scope would likely mean a huge amount of time/negotiations to fully realize.