You've effectively answered your own question. The problem is clearly related to poor signal strength.
TV transmitters are designed on the assumption that viewers will have good quality
external aerials. There has never been any intention (from the very first days of TV broadcasting) that people should be able to get good reception with indoor aerials. Obviously where people live close to high-powered transmitted they might be able to get away with using an indoor aerial but it's definitely 'not part of the plan'.
Further, different TV receiving devices (whether they be TV sets, video recorders or whatever) have different 'sensitivities' (i.e, their ability to handle weak signals). It's not uncommon for people to find that one TV set in their house [with decent sensitivity] gets excellent reception while another TV set [with poor sensitivity], fed from the same aerial, struggles to receive anything at all.
The only guaranteed solution here would be to get a good quality external aerial installed. However, given that there are currently a few channels being picked up, a signal booster might possibly do the trick. Large supermarkets sell them for around a tenner but their 'gain' is nowhere near as good as this one, which is what I'd go for (and, indeed, is what I actually use myself!):
http://www.maplin.co.uk/p/1-way-aerial-amplifier-rt67x