To quote UK Fossils, picking out a few of the many areas they suggest where Fossils are Common or Often Found in the North:
The North of Wales is well known for is Carboniferous limestone rocks. These rocks contain fossils of corals, brachiopods, and crinoids. Some of the most popular areas to collect are on Anglesey. The best locations here are at Caim and Great Ormes Head.
Areas include: Caim, Great Ormes Head, Moel Findeg and Burley Hill
The Yorkshire coast is the second most popular area in the UK for fossil hunting. The same Jurassic fossils, famously found along Dorsets heritage coastline can be found here.
Areas Include: Port Mulgrave, Kettleness, Whitby and Saltwick Bay
Most of the fossil bearing sites in the Midland and Grampian of Scotland area are along the Eastern coast. Here, the Carboniferous rocks yield plant remains, brachiopods, trilobite tracks, giant millipede tracks, corals and crinoids.
Areas Include: East Wemyss, Crail, Kinghorn and St Monans
UK Fossils have a good map where you can pick a location (eg, North Wales) and it will list all the areas where you can look for fossils, how common they are, and what period the fossils are from.