Coming from Tatenhill you simply need to use the new 'North West Transit Corridor' (Manchester Low Level Route to us oldies) and then head towards Blackpool calling Warton on the way. Be prepared to be asked to route via Southport/St Annes pier not above 1500' and then join the circuit in accordance with BPL ATC instructions. It's a well worn route for many from Barton and the South. Read up on the new corridor rules.
Your other option is to enjoy a grand view of Liverpool City centre by heading for Tarvin Roundabout and asking for zone transit to Seaforth Docks. Avoid the ATZ at Woodvale, it's usually active, and then head to Southport pier as mentioned above. Liverpool are great with transits and rarely refuse. That route will take you right up the Mersey at 1500' or below. Have your camera ready.