Can anyone recommend a charming, but budget/modest hotel/B&B in the FITZROVIA neighborhood for June 2018?
Have a look at the Rathbone Hotel or the Grange Hotel Fitzrovia and see if either of those work for you. Oh, also the Grange Langham Court. It’s not a cheap area but it’s a great part of London to stay in. I find the Rathbone particularly charming in an undefinable way, and I’m always happy to stay there.
The Astor Court Hotel - on the cusp of Fitzrovia & Marylebone - is often very cheap and perfectly pleasant, if tired around the edges.
You could look just into neighbouring Bloomsbury at the Arosfa on Gower Street, too.