The RSPCA can remove animals under the Animal Welfare Act but only if they have an 'Inspector' with them. That's someone appointed by the local authority (often an animal warden) not necessarily an RSPCA Inspector (that's a different job title). They can also take animals away if the owner agrees to sign them owner.
The act makes it a duty of care to provide:
* a suitable environment (how it is housed);
* a suitable diet (what it eats and drinks);
* the ability to exhibit normal behaviour patterns;
* any need it has to be housed with, or apart from, other animals; and
* protection from pain, suffering, injury and disease.
The guidelines for rabbits have not been finished so there are no set rules on what a suitable environment for rabbits are though 5'-6' hutch is considered suitable by most welfare orgs.
If the RSPCA find an owner not meeting one of the duty of care's then can issue an improvement notice. That's basically a document saying what the problem is, what should be done to correct and a timescale to do it.
These might not be issued if the animals in immediate danger.
If the person failed to complete the items in the improvement notice then the rspca (or animal warden) would seize the animals and may prosecute the owner under the act.
More info here:
http://www.defra.gov.uk/animalh/welfare/act/affect.htm#9
http://www.defra.gov.uk/animalh/welfare/act/index.htm