Will IBKR's commissions and fees change when my account is migrated due to Brexit?

No. IBKR commissions and fees do not vary by the broker your account is maintained with.

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Is my account restricted from being transferred to another broker if I have an open Intraday Margin Deficit (IMD) despite being in end of day margin compliance?
Dividends and distributions: If I own foreign securities in my IRA and there is a foreign tax withheld, may I claim a foreign tax credit?
Do you charge a fee for an IRA account transfer out?
How do I fund my account after Brexit?