You say "a Saturday morning". What Saturday morning is it?
In most cases 6 am on a Saturday will be quieter than 6 am on a weekday as you won't get many business travellers. But if it's a Bank Holiday week-end, or the beginning of the school holidays, things could be different. I once made the mistake of travelling from LHR on the Saturday of the February half-term holiday, and it was like a zoo. (Not having children I didn't realise it was half-term...)