Italy being the birthplace of Reinassance, there is the time difference between the Renaissance period in the countries in question. Obviously, the Reinassance started earlier in Italy, around 14 th century, while in England it started in the 16th century( some will say that in began earlier then that).
The height of the English Renaissance was during the so called Elizabeth era. The poets, playrights and writers were often paying tribute to the queen Elizabeth and she was often a patron to them. The Renaissance concept of admiring a lady far above your self is interesting in this respect, a female monarch as a patron is certainly a fascinating subject of study. So, here it is how a concept imported from Italy, sort of say, was adjusted on the local level.
On the otherhand, at that time the Italy was not unified, so it would be hard to pin down the exact centre of Reinassance. I do not think that the Italian writers did circle around one patron, rather there were many different patrons, such as the famous Medici. So, the political conditions were different in Italy and that reflected on art as well. Italy was at the time the most urbanized nation in Europe, where cities often were self- sufficiant (like ancient Greek cities). England on the other hand, had a traditional monarch and the capital that we could call the centre of cultural activities.
The theathre was a part of the Italian Renaissance, but not in a way that it was in England. The tradition of English Renaissance theather is very unique. As far as I know the plays in England at the time were watched by a wide range of people from all classes. Again, the queen Elizabeth played her role in ensuring good conditions for theathre to blossom.
As every language is different, there are differences to be found in terms of literature, such as in poetry. The Italian sonnet had to modified to be used in English. Moreover, the English poets did not just copy the themes of Italian poets but started to develop their own in time.
There is the difference in the religion aspect that is significant for cultural aspect of Renaissance. I advise you to reasearch differences between Protestant and Catcholic religion and see how that reflected in arts, literature included.
There are some other differences in other art forms. In England the emphasis was on literature and music. In contrast, in Italy, aside from literature and music, visual arts and arhictecture played an important part in the movement.
Italy as a birth place of Renaissance was the model for other European countries as well. The popularity of Petrach, for example, was at that time unmatched by any other poet from any other nation. Italy was a sort of role model for other countries, where like in England , the art movement has spread. England understandigly could not be the role model since Italy was the first.
I'm sure that more can be said about this topic, this is just a short list of some of the differences. I did not go into detail, I'm not sure is that what you were looking for. I'm sure if you research on internet a bit, you'll find even more examples for the differences between these two countries. In general, the art of every nation is always unique, reflecting the characteristic of its people, so it is not hard to find differences between two nations.