Public showers in Heathrow T1 and T3 -- experiences?

I've been reading in various other postings that there are public
showers available at Heathrow Airport. (The most recent one appears
to be in alt.travel.uk.air in March 2002). It seems that showers are
free, but I can get a towel at the Information Centre for a pound or
two.

Could someone with recent experiences please refresh us. (There was
some discussion about construction going on).

(1) Are public showers still available in T1 and T3?

(2) Are the facilities better in T3 than T1? (I assume that I'll have
to clear immigration first, and then enter the T3 airside mall).

(3) Is there a way to store or hang hand luggage so it doesn't get wet
while I take the shower (and don't have to worry about things getting
stolen?)

I'm going to flying from Canada arriving in Heathrow Terminal 3, and
transferring over to Heathrow Terminal 1, with a four hour connection.
I'm pretty sure that I have enough time to get a shower, if I don't
make mistakes along the way.