how do i send text messages over the internet to a uk mobile phone, o2

Does ICQ still do this? - chances are good.  www.icq.com

If you know which network the phone is on, you can try the providers
website.  They often have a means of SMS to their own phones.

A good pay-service is ipipi.com.

Nowadays, most mobile phone carriers have an email address linked with
their service, but with some of the smaller carriers, this is not the
case.

MSN Messenger has recently linked up with mobile phones, to send Text
Messages, so that if you were to log onto MSN with your co.uk account,
you'll be able to set up your mobile phone to receive text messages,
so anyone messaging you will be able to send it to your phone.  (keep
in mind that anyone on your MSN list will be able to use/Abuse this
function!  I learned from my mistake)

Use www.teleflip.com or do a search for "Free SMS"

try sms.ac