Google does that for you already.
The OS Maps App will let you record a route, on the free version too. It's handy too if you have paper OS maps with the code on them for the online version, as you can create a free account and add those to it and be able to download them to your phone and so can look at maps even without signal. While that might not seem any better than a paper one, it gives you your GPS location on the map, so rather than trying to work out where on earth you are, you can see (within the usual margin of error). I have it on my phone as a backup for when/if I get lost.
