There is no particular office I would say. Some patent offices have examiners more knowledgeable in some topics than others, then some examiners are better than others. You could file the same application twice with the same patent office and get two completely different search reports. Since no patent office guarantees a perfect search report, some applicants also request Supplementary International Searches in the international phase to check if other patent offices are able to retrieve additional prior art before entering into the national/regional phases.
Anyway bear in mind that national patent laws typically preclude you from filing the first patent application with any patent office. I do not know the particulars of the British patent law but I guess the first filing should be with the UKIPO, the EPO or the IB with some limitations regarding the ISA you can request. And this question aside, if you were to file your application with say the Chinese patent office, the costs would be significantly higher because you need the services of a registered Chinese patent attorney, and translate your application into Chinese, plus the search report/first office action would be in Chinese as well.