A broker is the firm that holds your account, quotes the prices you trade at, fills your orders and holds your money. For an automated strategy, the broker's contract specifications, spreads, execution and server time determine what the EA actually experiences, and the same EA at two brokers will produce two different records.
What regulation provides
In the UK, brokers offering CFDs and forex to retail clients must be authorised by the Financial Conduct Authority. That authorisation brings client money segregation, so your funds are held apart from the firm's own; the Financial Services Compensation Scheme, which covers eligible claims up to £85,000 if the firm fails; negative balance protection, so a retail account cannot go below zero; the leverage caps described on the leverage page; and a route to the Financial Ombudsman if a dispute cannot be resolved. The FCA register, searchable online, shows whether a firm is authorised and for what.
Brokers regulated elsewhere offer some of the same protections and some not. Offshore brokers offering leverage of 1:500 or more to UK residents are generally not FCA-authorised, and an account with one carries the risk of the firm rather than the risk of the market on top. Higher leverage does not improve a strategy's results, and for a risk-sized EA it changes nothing except the margin required.
Market makers and agency brokers
A market maker takes the other side of client trades and manages the resulting exposure itself. An agency or ECN broker passes trades through to liquidity providers and earns a commission. Both models are legitimate when regulated, and both have quirks. A market maker has a potential conflict of interest that regulation is designed to manage; an agency broker's spreads depend on its liquidity providers and can widen sharply. What matters is the price and the fill you get, and that can only be measured by trading.
What to check for an EA
Whether the broker offers every market the EA trades, under names the EA can be mapped to. The contract specification for each: contract size, point value, minimum and step volume, margin, swap, and trading hours. The typical spread at the times the EA trades, not the advertised minimum. The server time, if the EA trades on daily or weekly bars. Whether the account type is netting or hedging, and which the EA needs. Whether the broker allows EAs, scalping and news trading, since a few restrict them. And whether it provides or supports a VPS.
A multi-market EA trades eight stock indices, ten currency pairs and gold. Broker A offers all nineteen, with the Hang Seng and the Russell 2000 under its own symbol names. Broker B does not offer the Hang Seng or the Nikkei at all. At Broker B the EA can only trade part of its book, and its results will differ from the vendor's record for a reason that has nothing to do with the EA. Broker A's index point values are also a tenth of Broker B's, so the minimum balance needed to run the EA at Broker A is lower.
Choose the broker for the EA, not the EA for the broker. Start from the list of markets the EA trades and the account type it needs, and eliminate brokers that cannot provide them. Then compare costs at the hours the EA trades. Then open a demo at the shortlisted broker, run the EA for a few weeks, and confirm that the symbols, the fills and the spreads behave as expected before funding a live account. A vendor who publishes a live record will usually say which broker it runs at, and using the same one removes a variable.