Shop staff have no right to search your bag, even if they have a sign by the entrance or inside the store that says they can do this. If they ask to search your bag you can refuse. If they then use force to search your bag, they may be committing a criminal assault, and you may also have a civil claim against them for damages (compensation).
However, shops can require you to leave your bag outside the store before you come in. They can also require you to leave the shop if you’re inside.
Trespass Act 1980, s 3
Even if shop staff or security guards carry out a lawful “citizen’s arrest” for shoplifting and forcibly keep you in the shop until police arrive (see below), they still have no right to search you or your bag.