Ben Yearsley, who was a senior director at HL and now works for Fairview Investing, said he “can’t see any threat” to the business in Bristol.
He said: “I don’t see any benefit in moving it elsewhere. There are plenty of benefits from being a UK business, and the expertise of HL is its staff.
“Why would you risk that?”
The firm was founded in 1981 by Peter Hargreaves and Stephen Lansdown, using a spare bedroom in Mr Hargreaves’ house and a couple of borrowed desks.
Today it has 1.8 million customers who invest their savings and pensions with the company. In all, HL manages £1.55bn for their clients.
In the 1980s the two founders wrote newsletters to their clients, advising them of rising funds and investment tips.
The firm now has a high-tech online investment platform where customers can trade shares, monitor their pensions and more.