You could, but guessing would be good too :-)

Is it one of the stone structures in front of Euston Station? The ones with all the names of towns where the trains go?

Good idea but not there. Sarf...

East of London Bridge. (Hoping for a lot of guesses...)

BErmondsey?

A person rather than a place... (east of Bermondsey)

BEnjamin something?

Not Benjamin. It's the start of a surname rather than a first name. Searched for those who searched for the north-west passage...

BElcher?

Good guess but not him. There's not a lot left to guess...

E-bay?
Yes, hard to know where to pitch things here. I have put up a few easy ones and they've gone quite quickly - but perhaps that's more encouraging than hard ones. My last batch are hanging around a bit...

Come on you guessers!
It might be east but it's very tourist east...
There's not a LOT more I can do to help you with this but just add a L(ittle) to that clue and a bit of joined up thinking will get you the answer.
(I am determined not to send this to the graveyard.)

Is it in Greenwich?

Yes, Greenwich. Yes, close to the river. This is a LOT better. (Note what I keep saying!)

Trying to get a head, Bill? Mais non...