Also, we would join the European asylum scheme where we would only need to accept out fair share of asylum seekers. At the moment we get far more.
'At the moment we get far more'
What are you basing this claim on? The UK receives fewer asylum applications than France, Germany, Italy and Spain.
On a per capita basis (asylum applications per head of population), the Refugee Council recently put the UK in 16th place in Europe. The Migration Observatory puts us in the range 13th to 18th place in the EU/EEA area, depending on the year, over the last five years. The European Union recorded over 4 million asylum applications in the last 5 years (not including the scheme for Ukrainians).
And what about secondary migration of refugees once they have gained EU citizenship? For example, around a third to a half of Somalian refugees who were granted refugee status in countries such as the Netherlands, Sweden and Denmark, subsequently moved on to the UK with EU citizenship (several tens of thousands of them) - one of the reasons being that they wanted to live in their own Somali communities, whereas the Netherlands and Denmark in particular tried to force structural assimilation.
We didn’t have to accept the mass immigration we had under Blair and it wouldn’t be repeated
It has been repeated already.
Tony Blair put seven-year transitional controls on Romania and Bulgaria when they joined the EU in 2007 - the controls expired at the end of 2013. Ultimately it made no difference - more than a million Romanian nationals have applied to the EU Settlement Scheme and several hundreds of thousands of Bulgarians.
The seven-year transitional constraints deferred rather than prevented mass immigration. In turn, Albania and Ukraine are very poor countries - Ukraine was the poorest country in Europe even before the war started, and the UK has returned more Albanians who arrived by small boat than any other nationality. Of course they will come in their hundreds of thousands, perhaps a million or more.