Which universities have the best modern language departments?

Depends what language(s) you want to study.

Generally, SOAS is the next best after Oxbridge for most Asian and Middle Eastern Languages (and debatably better for actual language acquisition purposes - it also has a very strong profile internationally, much more so than domestically, in the countries whose languages it offers). Unfortunately the recent restructuring has limited some module options a bit and perhaps blunted this lately, but I've not heard anything absolutely devastating to come of it (for the languages that survived anyway...sadly not all did...).

UCL is quite well regarded generally and offers quite a few European languages not offered elsewhere (most of the SSEES languages and the various Scandinavian languages in SELCS), so is well worth considering too. Also depending on your course you may be able to take modules from SOAS while at UCL giving you even more language options!

Outside of those, Leeds is well worth considering as they also offer a wide variety of European languages and also a number of Middle Eastern and perhaps uniquely (now that SOAS has cut a lot of their options for that region) , South East Asian languages. Sheffield is notably one of the few places you can study Korean outside of SOAS and Oxbridge, and they offer a number of other languages too (apparently the Japanese course is supposed to be fairly decent too).

This is very helpful and I greatly appreciate it. I am wanting to study French and Spanish (from A-level) and ab initio Portuguese. Leeds only allows you to study two languages so I've eliminated it on that basis (along with Manchester, York, Bath and Durham for the same reason). As a Londoner, I'm also keen to study elsewhere so I've ruled out all the London unis too (other than perhaps Royal Holloway) plus Warwick (campus is too remote). I really am stuck between the ones on my list!

Predicted AAB but that's ambitious - I'm definitely not Oxbridge material! I fear ABB is more realistic. Thanks about Leeds - just checked and you can study a third language in your first year only.

Leaving aside Oxbridge and the Scottish Universities, which unis are strongest for MFL? I have looked at The Guardian guide but it is inaccurate - it rates Nottingham Trent 16th for languages but they don't even do languages!
FWIW, I was thinking of applying to
1. Exeter (AAB)
2. Nottingham (ABB)
3. Either Sheffield, Southampton, Birmingham or Liverpool (ABB)
4. Another one from the list above
5. Reading or Swansea (BBB insurance choice)
Any help would be appreciated. I thought the Guardian guide would help but have lost faith in it!