No there is no such connection, there are two badges you may find on a P1800, a swooping J with a blue and yellow striped shield and crown on the C-post on the 1960-62 models made by Jensen in the UK and on later models the 1800S-shield next to the rear lights which show that the car was made by Volvo in Sweden.
Jensen was a small manufacturer and had a hard time keeping pace (production targets were 10 000 cars a year) and quality was poor for a number of reasons, beyond the logistical and manpower-related problems there were also confusion related to Jensen using imperial and Volvo ordering a car in metric and uninterested suppliers. The car is very british, the metal came from Pressed Steel, the electrical system were Lucas, the carburetors were Skinner Union and the brakes were Girling.
Volvo was so unhappy with the quality they decided to ship every finished car from West Bromwich to Gothenburg for quality control before shipping it to the customer and after two years decided to give Jensen a bunch of money to get rid of them and make the car themselves instead. And that's why they stuck that badge on, to show that the car was a "proper" Volvo. Many enthusiasts think the Jensen cars are a little more exciting because of their "british" character although most agree the later models are much better made