Depends on a number of things;
1. Your experience on joining.
2. Your chosen/ allocated base on joining.
3. Your desire!
So, for instance, when I joined I came with about 1000hrs 757 experience elsewhere. My base was Manchester and during the summer they have more 767s based there than 757s, so upon completing my 757 operator conversion training I went straight back into the sim to do the 767 conversion and flew the 767 virtually from day 1. Longhaul is done on base/ seniority and it took about 12 months to get onto the longhaul list.
If you join on the 757 with very little other commercial experience and are Manchester based, you will spend a lot of the summer flying out of other bases and they won't convert you to the 767 until about a year of 757 experience has been gained.
PP