The police can usually only search your home in one of a few situations: with your genuine consent; with a search warrant issued by a court; or using a specific legal power (for example, to search after an arrest, or in an emergency to protect life or prevent serious damage).
If they rely on your consent, it must be informed and in writing where practicable, and you can refuse — they should tell you that you do not have to agree and that anything found may be used in evidence. You can also withdraw consent.
If they have a warrant, it should be shown to you, and you are entitled to a copy. The search must stay within what the warrant allows — they can only look in places where the items they are searching for could reasonably be.
A search must be carried out at a reasonable hour unless that would frustrate its purpose, and with no more force or disturbance than necessary. Afterwards, the occupier is entitled to a record of the search and a list of anything seized.
This is a plain-English summary. For the exact rules, read the official PACE Code B.