There's this awesome tool called Orbis. You can plot pretty much any journey you like, indicating starting point, destination, transport mode, season, and so on. It will then tell you how long it would have taken, what distance would have been covered, and how much it would've cost (approximately).

For your specific question we can put in Roma (Rome) and Londinium (London) with default settings to get this result:

The Fastest journey from Roma to Londinium in July takes 27.1 days, covering 2967 kilometers.

So that's four weeks, most of it by ship.

Note that Orbis is a model of the Roman transport network and is not 100% accurate. It is based on ancient sources though and does give a pretty good idea.

Found this made by Stanford which calculates how long it would take depending on month and means of travel etc. According to this site it would take around a month. Not sure if it's what you're looking for, but I hope it helped somewhat.