If you're looking for a meeting place or a good stop around ½ or halfway between Birmingham and Liverpool, you can try Keele, United Kingdom, which is almost an hour northwest of Birmingham, or about 1 hour southeast of Liverpool.
About ¼ or a fourth of the way, you can stop at Cannock, United Kingdom. This is about half an hour north of Birmingham.
About ¾ or three fourths of the way, you can stop at Warrington, United Kingdom. This is about 1½ hours northwest of Birmingham, or about half an hour east of Liverpool.
If you drive straight through without stopping at all, the total distance is 163 km. The distances shown above don't include local roads to get into each town, so if you're planning a long road trip, make sure you factor in traffic and road conditions, rest stop breaks, and interesting detours along the way. If you're in a rush, you can do the trip with zero stops, and your total travel time would be around 2 hours, 5 minutes.