Eurostar trains that run for Eurostar are maintained at North Pole depot
which is in inner north west London. You can see them from the Great
Western Main line from paddington. They use the West London Line to near
Clapham Junction and then the main line into Waterloo.

I suspect you may be referring to the Eurostar sets used by GNER for the
White Rose express services. I think they are maintained at Bounds Green
depot where most of the GNER fleet is maintained. There are smaller
facilities to deal with minor servicing of GNER trains at Newcastle,
Edinburgh and IIRC Leeds.

I knew it was in Herfordshire somewhere.......
Wouldn't it better to build a depot somewhere on Waterloo line?
Isn't their space around Wimbledon?
Or even the one by Three Bridges in Sussex? I think Gatwick Express or
Virgin use it?