Advice on 'stop overs' please?

Hi, I have only recently started caravaning and was wondering about random stopping on-route for sleep/rest.  Can anyone advise if caravaners are able to stop for a few hours in motorway services (perhaps in the lorry bit)?

I know we could stop in parking laybys but thought it may be safer in a services but not sure if allowed.

Also, can anyone advise on the general reaction from camp sites about letting people stay over perhaps in a car park whilst on-route?

Thanks