Head to your local library and ask for the Writers'and Artists' Yearbook 2006. (It should be in almost every library. You can buy it from most bookshops for �13.99 but you only need pages 465-468 so photocopies will be cheaper!).
The pages referred to, above, list all of the main greetings cards publishers in the UK. The listings not only provide contact details but indicate the type of freelance work that they're prepared to consider. Many state 'No verses' but some have entries such as 'Considers humurous verses' or 'Rhyming and prose verse 4-24 lines long'.
The W&A Yearbook 2006 also contains an article, "Winning the Greeting Card Game". (Pages 461-464). This is aimed primarily at artists but much of the information would still be relevant to those submitting verses.
Incidentally, Clintons are solely a retail company and not a publisher. The entry for Hallmark reads "As there is an in-house editorial team, only humour writing submissions will be considered".
Chris