Have been a few times now, Dusseldorf is a bigger airport, train and hire car both options from there.
Germanwings fly Manchester to Cologne for a cheaper option, airport is a bit smaller but nice if I remember.
Never flown to Liege, but have caught the eurostar from London to Brussels and then on to Liege, they regularly do a “any mainline Belgium station” for the price of Brussels offer. About 30 mins from Liege to Aachen on the train.
The time from London to Aachen by train is comparable to air if you take the mucking about in the airport time. So a bit longer from Manchester but you get extra eco points.
Lovely city though.. Enjoy