There’s a couple of ways you can do the walk. I’d advise walking out through the staff/goods entrance, rather than the main entrance (if you’re heading out or back later the main gates will usually be locked anyway and all traffic gets sent via goods in and the security lodge). It saves a decent chunk of the road with some of the hairiest corners. You can cut across the Express/disabled carpark to get onto the access road, which saves a bit of time if you’re leaving Towers Street at the end of the day.
Once you get down to the Chained Oak B&B you can also go down the path there, passing the tree itself and meeting the old railway. Then you pass The Ramblers Retreat and can follow Red Road (barely any traffic on that one and much safer to walk down than Farley Lane).
Another option for getting down to the village is to walk towards the back of the Enchanted Village, heading for its car park. Here you’ll find a public right of way.
Make sure you get on the actual path, not the more obvious looking entrance on the bottom corner of the car park (this will only take you to a bit of wasteland used by the park!). Follow the public footpath and it’ll take you behind the hotels and down the hill. You’ll go over the end of the valley the gardens are set in, before the path merges onto the old railway route, passing a small solar farm and the water treatment plant. Eventually you’ll come to Alton bridge itself, where you can use the road bridge to cross over to the pubs.
We did both at Fireworks last year as we had a cottage in the village, just round the corner from Alton Bridge and The Talbot, but wanted to enjoy a few drinks at the park without worrying about driving. They’re both pretty nice walks, though if you’re planning on going off of the tarmac I would recommend sturdy footwear (especially if it’s wet) and maybe carry a torch if it’s going to be dark! The public footpath from the hotels is a really good route to know if you’re stopping in Alton village and don’t mind a walk. As I say, it’s a public footpath and perfectly legal to use. No trespassing or anything like that.
Forgive the crude maps, but if you can grab the free Ordinance Survey Maps app from the App Store you’ll see all the footpaths clearly marked (it’ll also show where you currently are, so it’s easy to tell if you’re on the right path).