If the UK leaves the EU on WTO rules it will be the same as buying from any other part of the world. You will be liable for VAT and a handling charge dependant on carrier.
If the UK and EU come to a deal, we will find out when that deal is announced, we just don't know what the deal will look like.
Postage times will be dependant on how long it takes to process everything and apply said VAT etc. They will be doing it for everything sent to the UK from abroad. It will be the same in both directions I would assume