Baby in black cab and central London eateries with decent highchairs

[FeelingEvil]

I'm thinking of being a bit of a selfish mummy this evening by planning to take my 1 year old to a friend's art exhibition opening tonight (around her bedtime).
I'm going to carry her in the sling and hope she sleeps.
However, if she goes into meltdown I'm thinking of jumping into a cab.
Have never travelled in a car with her without car seat.
Will it be okay? Or is it against the rules?

Also, we'll be in central London - want to give her dinner before going to private view. Was thinking of taking her to Wagamama's but any other suggests as to where would be good. Want somewhere with decent highchairs.

Thanks

Here are the laws.

And don't feel evil, it's not as though you take her around London every evening. Enjoy yourself!

Thanks for the advice.
DD and I had a great time. She slept in sling on way into town, then we had a pasta dinner at Strada before making our way to gallery. She stayed awake whole time and was fascinated by cab ride home.
Must do it more often!

Great - I'm glad you both had a lovely time.