Since I read you have a Stocks and Shares ISA here is what I would do.

Sell all your shares which has no tax implications for you with it being an ISA

I would then transfer the funds to your bank account and then generate a statement for your application and wait till it's approved ( London Embassy doesn't need it sat there for long )

Once you have confirmation transfer the money back into the ISA and buy back into your shares.

** if your ISA account restricts you redepositing due to maxing your 20k for the year, transfer it to one which doesn't. For example trading212 allows you to withdraw and redeposit with no issue.