No.........as far as I'm aware all you would get through FOIA is a list of the numerical order of the prices of the tenders received - company names would not be part of this list
If the tender was published on eTenders website, there will normally be a Contract Award notice published sometime later, detailing the winner and (sometimes) the winning price. You might get more than this under FOI. Tenderers are usually asked to indicate if any parts of their proposals are commercially sensitive (which would avoid having them released). Smart tenderers indicate that the entire proposals are commercially sensitive.
There is no need to do this. If the tender comes under the EU procurement directives (EC 2004/17/EC and 2004/18/EC), prior to the publication of the award of contract notice and the conclusion of the contract, there is a 14 calendar day period (this can vary) at which information on the award of the contract must be communicated to all bidders, during which unsuccessful tenderers are able to seek further debriefing. Thereafter, an award of contract notice must be published in the OJ within 48 days. You can seek redress under the Remedies Directive, if your rights have been infringed.