Milan – Rome and Rome – Venice : train — it will be much faster than flying by the time you add time to get to/from airports (airport transportation leaves from the main train station) and check-in time to flight time.

Venice – Munich: fly or take overnight train

Munich-Prague, Prague-Berlin. Train will be as fast as flying.

Berlin-Copenhagen, Copenhagen-Amsterdam: fly unless you can’t find a reasonably priced flight.

Amsterdam – London: this one’s probably a toss-up. Take the cheapest.

There are some bus possibilites between Berlin and Copenhagen a tad over 5 hours. If you can find a cheap flight, go for it; but if not, then bus isn’t so bad for such a relatively short trip.
CPH-AMS: fly. It’s 11 hours by train.
AMS-LON: I’d fly. Train would go through Bru. then Par. before crossing over. I don’t have timetables open but I’d guess ~ 6 hours all-in for Thalys+Eurostar.

See skyscanner.com for cheap one-way flight hops.

Some Eurostar trains go directly from Brussels to London. Fastest Eurostar/Thalys between Amsterdam and London is 4 hours 40 minutes with a single connection at Brussels Midi. Some routings take as long as 6 hours 17 minutes, again with a single connection in Brussels. Difference is a longer wait for the Brussels connection.

Unless you have a burning desire to see something specific in Milan I would skip it and fly to Rome from Barcelona.

Ok that sounds reasonable, I had a friend who advocated going there but I was pretty impartial myself.

I could spend those extra days in Barcelona I suppose and maybe try and get out to some other Spanish towns.

Thank you for the suggestion.