I've seen both now and they are both worth while viewing.
As they both are part of a longer program, you might like to fast forward.
The Transatlantic Cable and the Great Easton, presented by Mark Horton, starts at about 45 minutes in, and lasts for about 10 minutes. Some footage taken at New Ferry with video effects of the Great Easton superimposed over the present shoreline (as per Time Team did). A demonstration with batteries and bulb is given on the beach, the principles of a moving beam galvanometer explained and a section of the cable is shown.
The piece on Birkenhead Park begins about 40 minutes in, with Nick explaining about ports not just exporting goods, but ideas, too, and hands over to Ruth Goodman for her article.
In it, Ruth talks to local historian Glynn Parry and walks, in part, around the docks, Argyle St South and Birkenhead Park.
It features lots of ariel shots of the park and makes the obvious comparison with New York Central Park, with some nice video effects of old and new. Also seen are old photographs of Charing Cross (Grange Hotel) and a couple of other pubs, including the Talbot.
Running time just over 6 mins, before moving on to Blackpool.