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)