In order to watch the inauguration of Trump in the UK, you'll need to pay/donate to one of Trumps businesses. This will ensure that you get a passcode so that you can enter it into either the mobile device you'll be using or provide it to your cable/satellite operator so that they can decode the channel for you. I do believe those companies along with the terrestrial ITV/Channel4/5 channels may also add an additional charge as well. I believe the donation/payment level is around the £199 level.
If you want to watch it in a pub etc, then you'll need to ask around your local area or further afield as to which pubs might have paid the commercial fee to Trump's businesses in order to show the event live and in public. The fee for that to pub landlords is quite high at around £7500, so be prepared for being charged an entrance fee of around £129-149 to enter the pub.
Cheers, DtM ! West London & Slough UK!