If we go strictly by the International Cricket Council (ICC) Test table, the answer is: YES. They are ahead of India by a point. That gap will only widen at the end of the series. If England makes a clean sweep of this series, they will have 107 points to India's 102. Other options: If New Zealand wins, then the British will have 105 points to India's 102. If the last Test is drawn, then the margin will be 106 points to 102. Based on those figures, it does show that the English have made more progress than India.
Now let us go by head to head competition. In the 2001-02 series in India, India won 1- 0, and the return series in England in 2002 was split 1-1. India 1, England 0. However, if we take their performances against different countries, this matter gets a different perspective.
Against New Zealand, India lost in New Zealand and did nothing worth noting in the return series in India. On the other hand, England drew first blood in the series against the Kiwis in New Zealand in 2001-02, with Fleming and crew winning the last Test to square the series. And we know what has happened on the return tour in England. England score on that one. India -1 England -1.
Against the West Indies, India lost in the West Indies 1- 2 and that too after drawing first blood. In the return series, at home, India won 2-0. Whereas the English defeated the West Indies 3 - 1 in England in 2000, and then won in the West Indies also by a margin of 3 - 0. Honours to England. India 1 England 2.
Against the Aussies, India won the home series 2 - 1 inflicting the first ever series defeat the Aussies experienced in a long time and then went to Australia, drew first blood only to lose the next and nearly win the third in a 1 - 1 split. The British though lost the home and away series by an identical margin 1 - 4. Here one can debate endlessly that the English played 5 Tests in every series, to India's three and four respectively. However, in a three Test series, one has a lot less time to prove their mettle and there is very little margin for error. So, if we go by the first three Tests between the English and the Aussies, the English still lose 0 - 3. India 2 England 2.
Both teams won the away series against Pakistan. England had a winning margin of 1 - 0 in a three Test series, whereas India's winning margin was 2 - 1. Honours even on that one. India 3 England 3.
England though has played Bangladesh and beaten them 3 - 0, whereas India has yet to play against them. If the Indians do play a series against Bangladesh and win, they will leapfrog the British in the ICC rankings. Some who read this article may argue the final score and I fully understand that. So, now the big question: Is England better than India? If we look at the structure of their first class cricket versus India's, they are years ahead. Every player envies the thought of playing in the English league.
However, with visa restrictions on "New" commonwealth nations, the Brits may well start denying visas in the future to select Asian players who they know will run circles around them. We all know who may very well be singled out in cases. Poor Muralitharan may be denied a visa for every overseas tour! That may very well give them the needed edge over India in the future. Time will tell. Until then who is better? The score is tied.