Up until fairly recently, license-free walkie-talkies could only use 8 specific frequencies within the 446Mhz 'PMR' (Professional/Personal Mobile Radio) band. As you've discovered, this could lead to interference. (When I was running a railway station, I frequently had to use the public address system to announce things like "Please would all staff switch to Channel 5, to avoid interference from the building site over the road")
Recently Ofcom have added 69 additional frequencies in the 433/434Mhz 'LPD' (Low Power Device) band. As your question appears to recognise, that means that the chance of interference is decreased. However it's important to note the 'low power' wording. PMR radios can use up to 500mW. LPD radios are limited to just 10mW. (That's because it's a shared band, which is also used by licensed radio amateurs). Consequently, the range of radios using the LPD band is less than that of those using the PMR band (at maximum power), but probably still good enough for your purposes.
Some radios which only work in the PMR band rather misleadingly refer to large numbers of 'sub-channels' or 'channel combinations'. Don't bother with them, because they won't solve your interference problems. You need to look for a reference to 'bi-band', 'LPD' or '433/434Mhz'.
Suitable radios include these:
http://www.maplin.co.uk/Module.aspx?ModuleNo=4 7345
http://www.maplin.co.uk/Module.aspx?ModuleNo=2 22222
Chris