Timothy is just one type of grass hay, but there are plenty of others to try. My pigs love Oxbow Timothy, but the Oxbow Orchard Grass goes down just as well.
Timothy can aggravate hayfever more than other hays, hence why I avoid it (can't be doing with itchy eyes and blocked nose when there's as good an alternative available!).
Meadow, Oat, Brome and Rye are a few other types of grass hays. It's the grass hay that is the best to be fed daily - not legume hays - so any kind of grass hay is just fine. Meadow is by far the most widespread and available hay in UK.