Been looking into this a bit more to find out exact times. Turns out the UK will only see the very end of the transit as it is finishing at sun rise. So if you want to see it you will need a clear view of the horizon to watch the sun come up at around 4.30am. Some more details from the RAS website below.
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Observing the 2012 transit: when, where, and how
NEVER LOOK DIRECTLY AT THE SUN, WITH OR WITHOUT A TELESCOPE OR BINOCULARS, WITHOUT USING A SAFE SOLAR FILTER. TO DO SO IS VERY DANGEROUS AND IS LIKELY TO RESULT IN PERMANENT BLINDNESS
The 2012 Transit of Venus occurs on 5-6 June, with the whole event lasting slightly under seven hours. The transit starts at 23:04 British Summer Time (22:04 UTC) on 5 June, after the sun has set in the UK. It will take about 20 minutes from the point when Venus first encroaches onto the disk of the Sun ('first contact') until the planet is fully silhouetted ('second contact'). The planet will then take a curved path across the northern part of the Sun. Mid-transit is at about 02:30 BST (01:30 UTC). Venus begins to leave the Sun ('third contact') at about 05:37 BST (04:37 UTC), and the transit will be over ('fourth contact') at 05:55 BST (04:55 UTC). Timings differ by a few seconds for different latitudes, but the transit will be visible from any place where the Sun is up (clouds permitting).
Unfortunately, this means that only the final stages of the transit will be visible from the UK. As a guide, on 6 June the Sun rises at 04:30 in Edinburgh, 04:46 in London, 04:51 in Belfast and 04:58 in Cardiff (all BST),
so observers in the UK will be able to see the final hour or so of the event.
Young people watching the transit of Venus in 2004, using approved solar filters. Credit: Charles Barclay
Venus is large enough for its silhouette to be just visible to someone with normal eyesight, without the help of binoculars or a telescope. Its diameter will appear about 1/32 of the diameter of the Sun. For safe viewing of the transit, the same rules apply as those for observing an eclipse of the Sun. Eclipse viewing glasses can be used, as long as they are undamaged and observing is limited to a few minutes at a time. Note that they must NOT be used with binoculars or a telescope. For an enlarged view, an image of the Sun can be projected onto a screen by a small telescope. Pinhole projection, however, will not produce a sharp enough image to show Venus clearly.
Observers should only use eclipse glasses that are marked CE under the EU Directive on the safety of Personal Protective Equipment. These are certified to conform to an agreed and effective safety standard. Under that specification the glasses or their packaging must be marked with any applicable obsolescence deadline (colloquially, the 'best-before' date). The capacity of eclipse glasses to block harmful radiations from the sun reduces with time. For example, glasses bought for the total solar eclipse in Britain in 1999 are now nearly thirteen years old and should not be used. In any case observers should inspect pre-used glasses for damage (scratches, holes, weakened mounting for the lenses...) and consider replacing them if there is a risk that their effectiveness in protecting the eyes is reduced.
http://www.ras.org.uk/education-and-careers/for-everyone/125
EDIT : Diagram for height of sun above horizon (in Edinburgh) below. Note 1 degrees is about the same distance as 1 diameter of the moon. So by 5.30am when its all over the sun will only be 7 degrees above the horizon. A bit a planning needed me thinks.