You need not worry about the sale of a share with a 20% gain creating a capital gains tax liability. Any trades on the same day are matched. I have sometimes moved positions between brokers this way: Put cash in Broker B where you want to hold the position. Open trading platforms for Brokers A and B. Ar the same instant place sell and buy orders in A and B. On a share with tight spread my loss can be 0, or just a pound. There is likely be a tiny capital loss, which can eventually be set against some other gain when computing capital gains tax.
You can try to be clever and buy in B for less that you sold in A, but I don’t try to do that. The point is that you can switch a position between brokers in one minute for less than some charge to do it over weeks (AJ Bell £25, Degiro 10 euros). Of course the constraint is that you can only move as much as you have free cash on hand.