Sadly a less transmissible strain will not succeed, as other strains take over. You can plausibly get a strain that is more transmissible and leads to less severe symptoms though, which would be delightful.
In fairness, not everyone is vaccinated, so those people might still have a severe case, as might someone who's just unlucky where the vaccine doesn't help them enough. High cases are obviously not desirable, but issues can arise anywhere in the world and not just in the UK.