I am planning a trip to London, with my boyfriend.

I have never been to Graineat Britain, and i´I'm very excited!

It's a good alternative name! ;)

However, my boyfriend whas inbeen to London twice.

So, the idea is to go the first week of March, and be only stay in London for around five days.

You can put 'only' before the verb: 'only stay' or at the end of the phrase: 'stay in London for around five days only.'

but iI don't have any more days of holidaysf.

or 'but I don't have any more annual leave.' or 'but I don't have any more holiday days'

I was looking for activities to do, and some of them are the following: Big Ben, Buckingham Palace, British Museum, Tower of London, The Shard Viewpoint, and Warner Bros.

Good options! :) Can I also suggest Madame Tussauds and the London Dungeons; also, some of these names need 'the' in front of them, i.e. 'The Tower of London' and 'The British Museum'.

I a’m planning a trip to London, with my boyfriend.

‘I am’ is technically correct but in written and spoken English the contraction “I’m” would be used

They a’re a couple and they met in Andorra eight years ago.

Using the contraction sounds much more natural

I ha’ve never been to Graineat Britain, and i´I’m very excited!

Great, not grain :)

Added contractions in

However, my boyfriend was in’s been to London twice. before

So, the idea is to go the first week of March, and be only in London forspend arboundt five days in London.

but iI don't have more days of holidays.

Always a capital letter for ‘I’.