The House of Commons Library, which provides a really excellent research service, has recently published a report on the whole local authority boycotts issue. This popped up as in issue in Brent when the Public Realm Contract was awarded (eventually to Veolia).
I got the impression at the time that many of the campaigners just didn't care whether what they were demanding was legal, so it is good to be reminded of the rules.
The EU Single market is essentially based on freedom to win and award contracts across national boundaries. There are detailed regulations in place to ensure this happens. Those regulations only allow companies to be excluded in very specific circumstances. For instance if there are convictions for corruption, fraud or human trafficking, or for not paying taxes. It is extremely hard, I suspect simply illegal, to ban a company because it has operations in a foreign country.
In the Brent case, this is in addition to the many practical difficulties of the proposed boycott which I pointed out before.