In general, you have a right to privacy/respect for your personal life on the part of your employer (and any other party), by virtue of the ECHR/HRA article 8. It is not unlimited, and your employer certainly has the right within reason to monitor use of its facilities to protect its own operations and to limit or prohibit use of company facilities/infrastructure for private communications where that could compromise operations, etc. What would almost certainly be considered an unreasonable breach of privacy would be any monitoring of communications that they did not tell you about beforehand, of the use of subterfuge to accomplish it (I can't imagine, for example, that password sniffing software would be considered reasonable unless there was a very serious security threat). This stuff tends to rely on notions of reasonableness and proportionality, so the circumstances are obviously important. Dismissal for making a phone call home from an office, for example, would generally be considered disproportionate; making the same call from the flight deck rather less so.
There is also some privileged status for communications to do with trade union activities and that sort of thing. Also spending your entire working hours browsing message boards for quite unrelated occupations is also unlikely to fall within the scope of the ECHR right, so it's lucky that I'm self employed really.
(does not constitute legal advice, etc. etc.)