Of course, my watch (and all Sat Navs) will still work if access was removed as they can still use the US GPS system and/or the Russian GLONASS system (assuming they were designed to talk to them already).
And there's no way they can remove access to the signals which the Sat Navs rely upon without shutting down the entire system. Leaving the EU means we lose access to the Galileo programme. Short of putting a huge tinfoil hat all the way over the UK, the EU can't stop Sat Navs in the UK, whether UK-resident Sat Navs or foreign Sat Navs being used in the UK, from using the Galileo signals for determining their location.
A feature Galileo doesn't have. The standard unencrypted Galileo signal allows location to be determined to +/- 1 metre, easily enough for Sat Navs. The only option to prevent people using that service in the UK is to turn off the whole system. Or deploy the tinfoil hat. Actual, not metaphorical.
And there's no way they can remove access to the signals which the Sat Navs rely upon without shutting down the entire system. Leaving the EU means we lose access to the Galileo programme. Short of putting a huge tinfoil hat all the way over the UK, the EU can't stop Sat Navs in the UK, whether UK-resident Sat Navs or foreign Sat Navs being used in the UK, from using the Galileo signals for determining their location.