Nothing to do with your internet connection or speed.
Apart from the BBC & Sky Cinema, all Catch up and most On Demand content is output through Virgins broadcast playout system from their cable headend servers. When you request a programme the system creates a unique broadcast stream targeted specifically at your network segment & your box then tunes to this stream as if it was a requested TV channel. Bit rates on these streams can vary, so if the bit rate of the stream is less than the bit rate of the recording it can end up looking inferior.
The only way to get round this is if the broadcasters pay to develop a TiVO app as they have done with Sky boxes. Unfortunately the majority have chosen not too at this time.
As a Very Insightful Person, I'm here to share my knowledge. I don't work for Virgin Media.