I've not done Venice to London, but Verona to London is probably close enough.
If you want to do it by train then I'd recommend taking the
DeutschBahn-ÖBB services that run to Munich via the Brenner Pass and Innsbruck, and then the sleeper to Paris Est and then Eurostar. There's a timetable
here (pdf). (Sorry I couldn't find a link in English about these services but there must be information somewhere on the
www.bahn.co.uk site.
The journey is fairly time-consuming but IMO much more pleasant, and less stressful than flying.
You could use the trenitalia regional services via the Brenner Pass but the DBB-ÖBB service is quicker and less hassle (and probably cheaper).
It isn't cheap though: the fares themselves are reasonable enough (if you book ahead) but bear in mind that you pay a whopping £30 for taking the bike on the Eurostar and a more reasonable €10 for each leg on the DBB.
There are loads of spaces for bikes on the sleeper service, but only two on the trains to/from Munich.
The other gotcha is that you can't book the bike spaces online - but the Deutsche Bahn call centre (UK number) will sort you out.
Bikes (even in bags) are specifically prohibited on the thello services. I did manage to get way with it on the services that were run by the predecessor company, but having narrowly avoided being thrown off a service and spent the night sharing my couchette with my bike I really wouldn't recommend taking the risk - especially when DBB-ÖBB provide a good-quality, bike-friendly alternative.