The Government's position is indeed that only those who claim asylum through 'safe and legal routes' will be eligible for asylum in the UK. This was set out by Sunak on the 13th in the House of Commons:
The only way to come to the UK for asylum will be through safe and legal routes and, as we get a grip on illegal migration, we will create more of those routes. We will work with the United Nations High Commissioner for Refugees to identify those who are most in need so that the UK remains a safe haven for the most vulnerable.
The intention, apparently, is that all those who claim asylum after entering the UK through illegal routes - such as a small boat crossing from France - will be removed to a third country like Rwanda (see this memorandum of understanding) where their claim will be processed. When challenged by Stephen Flynn of the SNP to 'outline one single safe and legal route' that an asylum seeker could currently take to arrive in the UK, Sunak pointed to the programs for refugees from Afghanistan, Syria, and other countries:
Lastly, the hon. Gentleman made the frankly absurd claim that we do not have safe and legal routes into the UK. In the last few years, we have made offers of over 450,000 places to welcome people from Afghanistan, Syria, Hong Kong and, most recently, Ukraine. That is because this is a compassionate, tolerant country, and it always will be.
Here, Sunak is referring to programmes such as the Afghan Citizens Resettlement Scheme, the Vulnerable Persons Resettlement Scheme, the Hong Kong British Nationals (Overseas) Welcome Programme and the Homes for Ukraine Scheme. These programmes gave refugees the option to apply for resettlement while outside of the UK - it seems that further programmes of this type are what is being promised for the future.
So Sunak is rejecting the allegation that Britain is abandoning its international obligations, pointing to these recent arrivals. He does however, admit that the establishment of further safe and legal routes will only be looked at after the Government "gets a grip on illegal migration". Whether these safe and legal routes will materialise remains to be seen, of course.