Nationally, about 3.4 million people meet eligibility criteria for the drug, but the NHS plans to treat only 220,000 over three years.
Ministers have confirmed that GP surgeries would receive a £3,000 bonus if they prescribe the drug.
A typical GP practice of 6,000 patients, will have fewer than 20 people qualifying for the drug in total, and year one funding is expected to cover only a fraction of that number.
The Lib Dems say Southend has some of the starkest health divides in the country, with a 10.5-year gap in male life expectancy between the most and least wealthiest areas.
Obesity is a key contributing factor, yet many residents cannot afford private healthcare or prescriptions, which can cost between £160 and £310 per month.