This is a question we are asked frequently and the basic answer is yes. Display Screen regulations provide eye test rights to any employee who habitually uses a VDU (including flat screens) as a significant part of their normal work. As a general guide some sources suggest significant means more than an hour a day.
You have to provide them only if the employee asks for an eye and eyesight test. This is a test by an optometrist or doctor. There is also an entitlement to further tests at regular intervals; the optometrist doing the first test can recommend when the next should be. If you have a lot of requests you may find an optometrist who will do them for free as then they might get a new client.
You only have to pay for spectacles if special ones (for example, prescribed for the distance at which the screen is viewed) are needed and normal ones cannot be used. Your obligation is to provide only basic spectacles as are required to provide correction for working at a VDU. So you are not obliged to pay for contact lenses, designer frames or special lens treatments. Some employers may choose to make a contribution (equivalent to the cost of basic correction) towards more expensive options but there is no obligation to do so.
The requirement to pay for tests or spectacles does not apply to self-employed workers but for them you have to provide risk assessments, make sure the works station complies with regulations and (perhaps by providing the publication below) about working at a VDU.
There is more detail at: http://www.hse.gov.uk/pubns/indg36.pdf