'Could you tell me if children's entertainers need a CRB criminal record check in the UK? If so, which one and how to go about it. Also where can I get public liability cover cheaply?'
Yes, if you are performing or working with children on any level, a CRB check should be performed. The service has now changed to be called a DBS check (Disclosure and Barring).
Although a CRB or DBS check is not required by law for self employed performers, local authorities and all schools will insist that magicians show them the relevant certification before they are allowed to entertain children.
There are many companies that can provide you with a CRB check in exchange for a fee. However, it is possible to get a check without any cost to you other than a free show. If you offer to provide your act via a charity, at no charge, not only is this a great opportunity to get your name out there and do some good in the community, but often the Charity will do the CRB check for you, as it is in their benefit.
You can get more information about this check on the .gov site here
With reference to liability cover, I personally recommend you check out joining Equity. Equity deal solely with performers so they are very knowledgeable with reference to all aspects of performing arts and the legalities. Also, they are recognized worldwide, and once you join they are only a phone call away, should you want any advice. The cost of Equity membership is tiered to your income as a performer, so it's a great way to get public liability insurance cheaply and all the other benefits and protection the union has to offer.