Capital Gains Tax - Uk

Hey all, this is a genuine question specifically relating to Capital Gains Tax in the UK.

For those who may not know, we have to pay CGT on £12k or more per year. There is some weird algorithm they use, but if we are talking figures of £100k+ then you are looking at losing circa 20% on CGT.

I understand fees, taxes etc, but i genuinely don't understand why CGT is so much given that the gov are not active in my investment at all. But that's not my question - more of a rant!

My question is;

I brought around half a BTC a while back and subsequently that bank account has been closed that I made the purchase from.

I know that when when / if I sell my BTC off for fiat, the tax man will come calling. I am a hodler and expect to hodl for at least 12 years.

As per GDPR my bank would have destroyed any information they have one me - If they haven't, I can request that they do this in a few years.

If I sell my BTC off and the tax man comes calling for my CGT, what, in theory, would stop me from saying that I brought my BTC in cash for £400k and am now selling at a loss thus meaning that I don't need to pay CGT?

After all, HMRC wont be able to prove that I haven't, given that the original proof of transaction has since been destroyed by the banks as per legislation.

Any thoughts on this peep?

Thanks