Since the Bike Events brochure came in the post, I've been thinking
about doing the Manchester 100 ride in September.

Fantastic. Is it this one? URL:http://www.bike-events.com/m100.htm
Might even see you there.

I'm a very overweight 30-something who mainly uses her bike for
pootling to the shops and such. The furthest I usually ride is about
5 miles.

Looking good...

Oh and my bike is crap (tho there is a possibility I might
be getting a shiny new one in July).

Yay!

How realistic is it that I could be able to cycle 62 miles in one day
by September? Obviously I'd need to train/practice, can any suggest
how much and how often?

Easy job. You already seem to be riding a fair bit - carry on doing that
but up the pace a bit. Maybe ride to places instead of driving or
walking there. You're a lot fitter than you think, and upping the pace
will give you more of a workout, better lungs and really nice legs.

Longer rides would be an idea too. If you've got some countryside near
you then just whizz off round them. If you're local to Manchester,
URL:http://www.bicycledoctor.co.uk/gr_intro.html have a "dawdling" bike
ride that might suit - rides of between 30-50 miles with plenty of cafe
stops. Takes all day so little chance of them going to fast.

Between you and me I suspect you could just hop on the bike and do it
straight off, but it might not be such an enjoyable experience :-)