I found my first six caches using more or less the methods that you describe, without a gps. By then, though, I knew I was going to continue caching, and would sooner or later want to hide caches myself. For that, a gps is essential in order to be able to post co-ordinates for it.
I don't think there are many if any other cachers who never use a gps, but certainly there are some who rarely use one. For example, there's a cacher in the States whose number of finds is in four figures, and I believe he prefers to cache without a gps and only uses one where he feels it's essential.
I think you'll find it will become rather difficult when you try multicaches. I don't know whether you've looked at any yet (though I see from your profile that you haven't found any so far). With some multis you're given co-ords for all the stages except the last one on the cache page, and you may not have trouble with those (until perhaps the last stage!. But others only give you the co-ords for the first stage on the cache page. When you're out there at stage one of a multi and you've just picked up the co-ords for stage two, it's not that easy to locate the precise position on an OS map from co-ords of lat and long.
But I don't mean to put you off! I know from my own experience that it's extremely rewarding to find a cache that is supposed to need a gps, with only map, compass and hint!
Good luck with your gps-less hunting!
Do not go gentle into that good night.
Rage, rage against the dying of the light. (Dylan Thomas)