Sounds very much like a scam.
Maybe it's different in the UK, but that would be the first time that I've heard of a crypto exchange getting involved in the taxation process. Individual crypto-investors usually have the responsibility to self-report taxable events.
And as already mentioned by gentlemand, withdrawal fees are usually in the single digits.
That is a very big red flag, I hope you will return to this thread and do not ever comply to that. 300£ is a lot in my country, also wouldn't it be strange if they are asking for a raw numbers for withdrawals and not percentage of the amount you are trying to withdraw. Can you also plug the site and post it here so people can check out the credibility of the site, I know it is too much to ask but if it can help in preventing people getting scammed then please do plug the site and many people will thank you and many will be saved from these scammers if they really are scammers.