A small country like the UK can't have a big impact on something which runs all around the world (e.g. internet, bitcoin, ...).
I also don't believe we're going to see any impact, especially since it's going to be a lengthy process that is already making the headlines for years but...small country?

We're still talking about the 5th country in the world by GDP!!!
If people in UK wants to transfer money to people residing in Europe then they will need to exchange the currency which might be a burden.
Yeah, rather than changing pounds to euros they would change pound to
BTC and then
BTC to euros.
If the UK remains in the EEA they will still have access to SEPA which is pretty fast and cheap.