There is a difference between asylum seekers and skilled migrants (the latter is what every country wants, the former is where all the political heat is on).
On asylum seekers, in reality, the plan to move some asylum seekers to Rwanda won't work - its too expensive, legally dubious, and lawyers/charities will fight it tooth and nail. Its more of a political stunt and won't really do anything.
Up to now, the UK is very ineffective at removing asylum seekers. Overall, its incredibly expensive to remove asylum seekers from the UK and even when this occurs often lawyers/charities continue to fight for them to be returned to the UK. The UK, also doesn't require ID cards, uses English, and 'still' has a very strong economy all of which are massive pull factors for 'asylum seekers'. When you look at the numbers of children from ethnic minorities in the UK its pretty astounding - we are going to see huge changes in the demographic in the next 100 years (note: that's ok, but its ok to be honest).
The only thing that 'may' have made a slight difference is ironically Brexit. Yes it looks like a disaster, but before Brexit lots of asylum seekers that claimed asylum in mainland Europe when they received permission to stay immediately moved to the UK for work opportunities (I don't blame them). But then again this may not work as Brexit has been such a disaster the UK really needs more workers to come and work in the UK.
Note: I am neutral on 'asylum seekers' in the UK. Its a massive political hot potato and generally avoid all newspapers views on them - but the left and right newspapers are both pretty bad at talking about all this in an honest way.