Is it illegal to hold a child or baby on one's lap in a taxi?

I should clarify and say that I want to have both of my children (toddler and baby) in car seats in a taxi.  Particularly as we are planning a 40 minute ride to the airport and must take the M40.

But my husband doesn't want to carry car seats around and thinks it's safe and legal to hold our children on our laps as we go.

Anyone enlighten me on this?  I thought in the States this was not legal but I could be wrong.

Safe?  Probably not particularly, but then again, probably not less safe than holding them on your lap on a bus.  Is it a short journey?  Or can you phone a taxi-firm and ask if they have any taxi's with car seats?  They might, or they might agree to hold them and then pick you up on the return journey.  Not sure, but it might be worth asking. 
Legal?  Yes,  I believe the law is that they must be in a car seat if it's available.  Which means if you have it you have to use it, but if you don't have one, well.  Or that's what the law used to be.  Someone correct me if I'm wrong. 

This is what I found

Taxis and Private Hire Cars
The law is exactly the same as for children travelling in cars.

Taxis and private hire cars - Children under 3 years old

If carried in the front seat, an appropriate child restraint MUST be used (the adult seat belt is not sufficient)

If carried in the rear seat, an appropriate child restraint MUST be used, IF AVAILABLE.

If an appropriate restraint is fitted in the front of the car, but not the rear, children under 3 years old MUST sit in the front and use that restraint. (Remember, you could move the restraint from the front to the rear if you wish, and you should do this if you are using a rearward-facing baby seat and there is a passenger airbag fitted).

I'm not sure that entirely answers your question, but it's from from http://www.childcarseats.org.uk/law/index.htm where there's a lot more information.  As I read it ... if you have no child seat available and the child is under 3, lap is legally acceptable BUT DANGEROUS ... if you have no child seat available and the child is 3 or over then the adult belt must be worn BUT THIS IS NOT AS SAFE AS A PROPER RESTRAINT.

Why not book a car ahead of time and stipulate that you require child restraints / seats, stating the age and number of the children?

Edit to add - Mindy - sorry - didn't mean to "overpost" you there. I was still thinking when you had thunk

Thanks Graham.     You said what I had said, only better. 

Thank you all!

Yes, the taxis will allow us to install our seats.  I don't know about holding them for our return but you're right, the odds are good they would.

I'm kinda a worry wart and am freaking out about my babies in cars without proper restraints at any time.  We certainly have taxi'd around London with me holding baby, toddler in the stroller with wheels locked and my DH holding onto it securely, but I don't breathe easy in those rides.

I think our best option now is to drive our own car to the airport and park there.  Leave the seats in the car for the way back and not bother with the cab.

Might I ask a related but not UK specific question:  we are going to Paris - is it possible to train/walk/very short taxi around there and avoid taking the car seats?  With France (maybe it's Paris specifically) with the highest auto fatality rate in Europe, I'm really scared about going there without proper car seats.

It's sometimes a lot more appealing to just stay home.  But then, once my kids are grown, they will badger me, 'why didn't we go anywhere, mom, when we lived abroad?!' and I'll have no answer!

You should be fine walking and taking the Metro with a baby and toddler.  I've done it with little kids and a toddler in tow and don't recall any problems.   It may be too late, but there's a really good book-'Take the kids to Paris/Disneyland'  that has tons of useful info about what to do/how to cope with kids in Paris. I'd highly reccomend it. 
 I agree, I think your best bet is to drive to the airport and park.  It'll save a lot of hassle.