Can I buy an IPL franchise?

Why don't the IPL teams have English cricketers?

There is no specific reason for excluding English players from the teams. If it were, they would not have come up for auction, which they clearly were. Players like Alex Hales were up for auction and not offered by the franchisees. There can be several reasons for this:

  1. Balance the side, the fact that only four foreign players are allowed in a game. (Shaun Marsh had been productive for KXIP, but he was on a bench for the entire season)
  2. Unavailability of players. If you look at the teams, aside from big names like Malinga and Perera (big names in T20 at least), there wasn't much participation in Sri Lanka either. This was due to the recently completed Sri Lanka-England ODI series.

In a total of 8 teams, each with 4 foreign players, you have 32 international playgrounds. Countries competing for these spots are 8 (with the exception of India and Zimbabwe and assuming only players from the top 10 of the ICC rankings will be included in the auction; Ryan ten Doeschate is an exception).

8 countries, 32 places. Australia has the Big Bash League, which produces T20 talent, and so does West Indies. There are numerous examples of big names coming out of these tournaments and making them big, but few such examples from England.

The Indian franchises are more willing to spend their money on current international players and those who they see their performance in local T20 leagues.

KP recently retired and a big name with a reputation for crossing the line. So he was picked up.
Many other big names like Jayawardene and Sanga weren't picked up like Hales.

I don't see any official or discriminatory reason if this was part of your request.