The meaning of "they have much to be modest about" is the same as saying, "the British have accomplished many things, therefore they can be modest about many things". It is a compliment.

Bill, thanks for your opinion. But I don't think the writer would like to insult British here. Could you read the following full context and give me your opinion again. Thank you very much. Americans are unflaggingly active, curious and loquacious. British academics who are asked what they are working on will tend to reply dismissively: “Oh, Gothic, vampires, that sort of thing.” They seem no more eager to discuss their research than to discuss their haemorrhoids. This is because it is thought bad form to jaw on about oneself and one’s work. I spent twenty years in an Oxford college without once hearing my colleagues discuss their work with each other in more than the most cursory way. It is also because the British are modest, and have much to be modest about. If you ask an American academic what he or she is working on, however, you should be sure to equip yourself with a folding chair, a flask of coffee and a thick wedge of sandwiches, since you are still likely to be there three hours later. If you are trying to pick your way through the traffic on Fifth Avenue with an American graduate student at your side, he is bound to ask you what you think about hermeneutical phenomenology just as a taxi is about to toss both of you over its roof.

I disagree with Sofia Jul. This is actually a sly insult. When you say that the British have much to be modest about, you are saying that the British have accomplished very little, and therefore it is perfectly appropriate for them to be modest. In other words, they have nothing to brag about.