"You must not copy, transmit, modify, republish, store (in whole or in part), frame, pass-off or link to any material or information on or downloaded from this Site without our prior written consent."
Have you taken a licence from Rightmove et al for the data usage?
Plus my pasting of a company's terms to ask whether the OP is in compliance is hardly likely to attract the ire of the company, whereas if I was Rightmove's lawyers I might have an issue with someone taking parts of my database wholesale for usage on a competing site.
I personally think a competitor aggregating results is a positive thing, but I was just curious as to whether this was done with a licence or not.