Where to leave luggage?

There are not any alternatives to the left luggage charges at Paddington

Since the Troubles there are no lockers.

You need to use Excess Baggage Company.

Wouldn't your hotel hold your luggage? I've never had one that wouldn't - just arrive when you get in and they hold your bags behind the desk until check-in. I've only had to use lockers or baggage storage when in town for a day, on my way elsewhere with no hotel in town.
If your hotel can't help, I'm pretty sure the Baggage Company is the only option, but I defer to the experts (who seem to be saying the same thing).

I think Mira has the solution. I've never encountered a hotel anywhere that wouldn't hold bags until check-in. Call/Email them up and ask.

We have the same problem for our trip in May. Also renting an apartment, will arrive 2 to 3 hours before we can check in. I'm going to check with our landlady closer to when we arrive but at this point its pay the fee or lug it around with us (not a good option).

Ah, my mistake. Still, it might be possible that there could be a closet or something you could stick them in temporarily. Its not like the place is a black hole until check in time. They just need the time to ensure cleanliness and that other guests are out. Check in with them.

The difference between being able to leave bags before check in at a hotel and leaving bags early at a rental apartment is that there will be someone at the hotel at all times. At a rental the landlord or their representative won't be hanging out all day, just in case someone wants to leave their bags early. Every rental I've had we all arrive at a predetermined time. And if Ruth arrived before a previous tenant checks out, they aren't going to want her bags there.

Depending on the size of the suitcases, some museums etc have their own paid-for left luggage service which may work out a bit cheaper.

Victoria Coach Station has left luggage at 4 GBP per bag for 24 hours.
http://www.tfl.gov.uk/gettingaround/1216.aspx

from Heathrow, take the tube to Hammersmith. transfer to the District Line (across the platform) and continue to Victoria. The coach station is about a 2 block walk. See map here:
http://www.tfl.gov.uk/assets/downloads/victoriacoach-by-foot.pdf

thank you all...sounds like we will have to leave it with the company...the rental flat refers you to them so I know we would not be able to leave it at flat. we were planning on doing hoho tour...so maybe we will have little breakfast at Paddington and then drop off luggage and take tour and just watch our time. Let's just hope the flat fairies are with us and we can check in early!

thanks Laura for that info...will have to figure out if that would work for us...being rush hour I was hoping to avoid tube with luggage & a tired 13 year old. :).