Travel to London, with a pram

Hiya, new to the forum but could use some advice.
I've just posted in the visa forum about travelling to London for my Consular Notification of Birth Abroad & Passport appointment.  We're not driving as we're coming from Bristol and that's quite a hike.
I'm fine as far as paddington, but using a pram on the underground seems like madness.  I was thinking it would be better to walk over as it's only a mile.  Or would other's suggest taking the tube, folding up the pram and one of us carrying the baby? 
Or should we take a taxi over?  Can you take a taxi without a car seat?
Any other travel experiences would be helpful.  And if there's already a discussion about this, please could someone point me over?  I did a search but didn't see anything.
Thanks!!

You can take a taxi or a bus without a car seat. Or you can keep the baby in the pram and you guys carry it up the steps, that is usually what we did.

Lots of women with prams take the bus. There is a reserved section for you to park the pram as well.

Lots of women with prams take the bus. There is a reserved section for you to park the pram as well.

I'll second the bus. I tend to see more prams on buses than the tube - at least with a bus you're guaranteed easy accessibility. Plus you never know what the weather will be like for walking that day. 

You can search for a suggested travel route here: http://journeyplanner.tfl.gov.uk/user/XSLT_TRIP_REQUEST2?language=en And if you go to the advanced options, you can select an option to exclude routes with stairs.

Or you can find the specific route information here: http://www.tfl.gov.uk/tfl/gettingaround/maps/buses/

Thanks for the advice.  I do take the bus around here, but can never depend on them being the buggy friendly buses.  Slightly annoying when you have to be somewhere and the bus driver won't always let you on.
I'll look up the bus route, which may be the best option.  I really hate the underground.  I blame the NYC subway.  The only subway system I like is in Boston.

I just posted something about this on your visa question, without seeing this first.

If you can manage the steps with the pram, the tube isn't bad, providing it isn't rush hour.  Commuters do not take kindly to prams and do not generally make allowances for them.  I can't think of which lines you would have to take to get closer to the embassy, but if you have to switch lines, you are talking at least a few flights of steps or escalators.   

Buses are pretty easy with prams, but they only take 2 at a time and if you have a big pram, you may find you struggle to get situated.   If there is already two on the bus, the driver should give you the option to fold your pram and carry the baby on and put the pram on the luggage rack.  BUT, don't be surprised if they just sort of say "I already have two" close the doors and drive off.  

If it is a nice day walking would be nice.  Just head towards Hyde park and walk along that to Oxford street.   It's just a few blocks of Oxford street.   That would be my choice if you aren't terribly pressed for time.  

We took the train from Loughborough to London for the embassy experience, and we took the underground for the rest of the journey.  Because there were two of us, it wasn't that big of a deal to haul the pram up and down stairs etc, and we even had offers of help from people when it looked like we might be struggling.

However, there are a LOT of little flights of stairs around.  I can't say exactly which stations we were in, but it was a lot of upping and downing.  If it's not rush hour, though, and you're game for the hauling (or, for the folding up the pram and doing the transferring while holding the baby), it's do-able.  (and, as others have mentioned, folding up the pram might figure in when taking a bus, as well.)

It's up to you, I guess!  Having two of you to juggle things makes the whole experience a lot easier, really.

I haven't navigated a pram on the tube in a while but it can be done.  Even if you are alone, honestly, someone will probably help you.  I can't count the number of times I've seen women pushing a pram alone and someone picked up the other end to help carry down the stairs.  Londoners aren't all assholes.