I'm not suggesting the English aren't patriotic, but compared to many other nationalities they're not in your face with it.
You wouldn't have British people aggressively screaming "UK UK UK" and waving British flags in your face like you sometimes get in America during sporting matches or patriotic celebrations.
I think outside of certain events like Jubilee celebrations and Royal Weddings, British people find patriotism for the sake of it distasteful and pointless.
I would describe the British as quietly patriotic. They're proud of their country and its history, but they're not going to scream it to the world or let everyone know they're British.
To suggest that patriotism in the UK is anything like patriotism in the US is just complete and utter nonsense. The British are patriotic, but they're no more patriotic on average than anyone else.
I think the reality is people incorrectly assume they because of the empire, British people are patriotic and arrogant. That is simply not the case. Many British people are reasonably proud of their country, but certainly wouldn't go around ranting and raving about how great their country is.