You can do it! Have you grown Cattleyas before elsewhere?
The most important parts of Cattleya culture is light and not too high temperatures. When it comes to temperature, people in England used to say that Cattleyas want the same day and night temperatures as people. As everyone else knows, you freeze all the time in England, especially at night unless it's between July and September when its too warm.
Whether you like living in England or not, it gives you an idea of how to culture almost 100 % of all Cattleyas . The exception is Cattleya dowiana that wants warm and humid conditions all the time. So I guess you probably have the right temperatures for Cattleya culture where you live. What you can do is to maximize the difference between day and night, both when it comes to temperature and light. Try to give them at least 12 - 14 hours of total darkness during winter and at least 10 - 12 hours of darkness during spring and summer. The temperature should reach around 70- 73 degrees F during night in summer and 60 - 69 degrees F during winter (lower end is better). However, the light and light variations are most important. I don't know how much light you can give them where you live. I think you should try some extra light during the day if nothing else works. Maybe you should contact Jerry Fisher at Orchids Limited because he knows a lot about the light situation where you live. I want to stress though that there are Cattleya species that will flower very well where you live and they happen to be more beautiful than most hybrids. These are Cattleya labiata, mendelii, mossiae, and warneri. (Note that labiate really needs day and light variations.) There are probably more pure species that will like it under your conditions. I would also like to suggest some hybrids related to England such as Cattleya Bob Betts. ---- vendor information removed -see faqs on posting----. Stay away from Laelia, both species and hybrids, because they want more light.
One of my first orchids was a Cattleya labiata. I was just around 20 years old and lived in Sweden at the time (very, very dark) and knew almost nothing about orchid culture. But the only thing I needed to do was to give it normal orchid care and, from September till October, I put a paper bag over the plant between 6 PM and 8 AM and it always flowered after that.