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Such services do exist, but finding a truly reliable one among them is also not very easy. Personally, the best and most reliable service for me is https://sms4you.net/country/united_kingdom/ which I have been using for quite some time and have never been disappointed. In addition, you said that you need a British number, I assure you that you will find what you are looking for on their website. After using a temporary number, you will be sure of the quality of such a service.