I think Britain has great values. My grandparents escaped Nazi Germany and my best friend is an ex refugee. We should be proud- we have freedom of speech, freedom of belief, we hold, mostly, the police and government accountable, we have democracy and elections are carried out properly, we have free healthcare, we have a welfare system which is a dank sight better than most of the world, we are a country who generally values education as we have a state education system, we are in general a quite secular country and we are generally quite an accepting country in terms of equality for women, gay people, trans people, people from other cultures than our own.
We haven't got a lot of stuff perfect- for example, the welfare system which the Tories appear to want to dismantle, but the point is we HAVE one. We aren't completely accepting- not even close in terms of full equality for women, there is still a lot of homophobia, transphobia, racism and so on in society, but we are a lot better than most of the countries in the world. We are, I think, a country where in general people can get on with things without constant surveillance and we have a lot of freedoms and rights compared to most of the world. Compared to the US (where I currently live- I'm still British though!) we have less tolerance of religious extremism imo. We have, even now, a very class based society compared to other developed countries, judging on class is a negative value we have, I suppose.
I think a lot of developed countries have a very similar set of values, but we do have different bits as well, and the mix of our particular set of values is what makes them British values kind of.