@bkero One of most important things for foreigners to understand about cycling in the UK is that the overwhelming majority of cycle infra exists to fill someone (who probably doesn't even ride a bike)'s quota.
As such, on-road cycle lanes are often best avoided on safety grounds (there's no legal obligation for cyclists to use them), and signposted cycling routes are likely to be indirect, convoluted, hilly, muddy or obstructed by anti-cyclist gates. Off-road paths in urban areas tend to be full of dog-walkers and other oblivious pedestrians, which makes for slow progress.
Minor roads are generally the best option. Something like https://cycle.travel may be useful for route planning.