The England national cricket team is currently ranked fourth in the ICC Test rankings, and fourth in the ODI rankings. Furthermore, England have won 336 of the 945 Test matches they have played and lost 273, with an additional 336 draws. So the answer, based on statistics alone, would appear to be, yes. They do.
That is almost like asing if the United States of America has a good basketball team. The Brits created the sport, so it stands to reason that they would have one of the best teams in the world. However, that doesn't mean the Indian team can beat them from time to time.
I personally think that The 1970s, for the England team, can be largely split into three parts. The early 70s saw Ray Illingworth's side dominate world cricket winning the Ashes away in 1971 and then retaining them at home in 1972. The same side beat Pakistan at home in 1971 and played by far the better cricket against India that season. However, England were largely helped by the rain to sneak the Pakistan series 1–0 but the same rain saved India twice and one England collapse saw them lose to India. This was, however, one of (if not the) strongest England team ever with Boycott, Edrich, D'Oliveira, Amiss, Illingworth, Knott, Snow, Underwood amongst its core.
I believe the English Cricket is in for some troubled times. Since Kevin Pierson was dropped the fate of the team is much less certain. He was a key member and without him, I think only time will tell if they can still be a great team without him as a player.
No, England does not have a good cricket team, because it is dwarfed by the other world powers, such as Pakistan, India, and Australia. Even so, Australia has not been as powerful lately as they were a decade ago, and India's governing body is not very strong. But England cannot seem to put a winning team together, despite all of this.