Opera North (http://operanorth.co.uk/)
Based in Leeds, Opera North also tours around the country.
Madame Butterfly (Puccini); Queen of Spades (Tchaikovsky) - I think both are touring around the UK at the moment, including Newcastle, Leeds, Nottingham and the Barbican in London. The Queen of Spades recently received some pretty good reviews in the Guardian and Telegraph. Both operas are recommended by the Guardian as being good for first timers - I can vouch for Madame Butterfly.
Reviews of Queen of Spades:
Scottish Opera (scottishopera.co.uk)
Not really familiar with this company, but they tour round Scotland. Productions of The Barber of Seville (until November) and Tosca (May/June 12) might be worth checking out.
Welsh National Opera (wno.org.uk)
I've not seen a WNO production, but I've heard really good things. Based at Cardiff's Millennium Centre, but also touring around the country.
They have a pretty good season this year including The Barber of Seville (Rossini) and Don Giovanni (Mozart), both touring until December 1st. Both are worth checking out as a first opera. Early in 2012 they will be staging La Traviata (Verdi) - and absolute must for anyone interested in any sort of music! It's in Cardiff from 11th February until 3rd March - then it goes on tour until 20th April. Seriously try and catch this if you can! In addition to this they have Mozart's Marriage of Figaro, running over the same dates in Cardiff and then touring. An interesting addition is Wagner's Tristan and Isolde - this will be in Cardiff in May/June and the Birmingham on 16th June. The season ends with Puccini's La Boheme from 1-9 June in Cardiff and then 13-15th June in Birmingham.
The above would be my pick based on what they're staging this season. Below are a few others worth checking out:
Birmingham Opera Company (birminghamoperacompany.org.uk);
British Youth Opera (byo.org.uk);
English Touring Opera (englishtouringopera.org.uk);
Glyndebourne Touring Opera (glyndebourne.com);
Mid Wales Opera (midwalesopera.co.uk);
OperaUpClose (kingsheadtheatre.com) - I've seen a production of Madame Butterfly at this Islington pub in north London - it was pretty good too!;