I am assuming you are talking about a two up two down with a kitchen/ground floor bathroom extension. A potential pitfall is that you may need to reverse the direction of the stairs - adding to the expense, also the foundations of the existing ground floor may not be suitable for building up on (not sure where I heard this- not an expert). If you don't increase the downstairs space it may feel disproportionate. Also if you don't have space to fit in an upstairs bathroom (which you would struggle with some of the houses) it may always feel like a compromise.
A better option for extension may be getting a two bed with an upstairs bathroom, which was originally a three bed, then doing an attic conversion. These have larger downstairs and "fit" the number of bedrooms better.
Obviously the whole "proportionate downstairs" / upstairs bathroom is a luxury that may not be affordable, and in the London property market you make do with what you can afford.
Currently it is hard to find good builders in the area, and they do reputably charge according to increased value rather than labour/materials - so you may find it not significantly cheaper than a ready made three bed.
I am not sure what Newham's position on granting planning for this is - it would be worth trying to talk to the planning department to get a feel for whether this is an issue.
Apologies for the ramble. In conclusion, if you find the right property it may work, but I would only do it if you can live in it as a 2 bed for a while, and am prepared for the upheaval of building work.