It's understandable that your imagination runs riot before the birth of your child - it's a huge personal challenge, especially if you are expecting your first baby - but worrying about having the baby in the back of a taxi or in the aisles at Tesco is one concern you can almost certainly put aside. For a start, there are many pre-labour signs that you can look out for which will give you time to assess what's happening and call your midwife team. Also, as the due date approaches, you are likely to be seen much more regularly (hopefully weekly) by your midwife team, and body changes that might possibly make your labour an emergency could be picked up during one of these check-ups.

Fear of not getting to the hospital in time
Even if you are having a home birth, you may have a fear of going into full-on labour before the midwife arrives.
For a start, this rarely happens with a first baby. If you are having your second or third, and your previous labours were quite short, then you may want to flag this up with your midwife team early in your pregnancy so it can be discussed. However, it's usually only in 'Carry On' films and the occasional article in the Daily Mail that a woman gives birth on the kitchen table or the bus!
Babies do arrive in all manner of ways - unexpectedly fast, painfully slowly, by emergency caesarian, or as planned in a water pool - and yes, very occasionally a woman will suddenly find herself in the throes of labour. But if just knowing that this is a rare occurrence is not helping allay your fears, there are a few basic things you can do to cover yourself:
Keep your mobile charged up in case you feel you are going into labour and you need to call your partner and/or the hospital.
Keep key phone numbers on you at all times during the last couple of weeks of pregnancy: your midwife, the hospital, the labour ward direct line, your GP, and any friends or family you might need to cover babysitting etc if you already have a child/children.
Make sure your partner understands your fears and is available - that he has notified work he might have to drop everything at short notice, he has passed up that overseas trip to a colleague, he isn't going on many boozy nights out that might rule him out of the drive to the hospital, etc. Also, make sure you have a stash of coins if you have to pay-park near your labour ward, and check your overnight bag is already packed. Feeling like you are getting everything neatly in order in your arrangements will help ease your fears of the unexpected.

If you do have a serious fear of going into labour too quickly, you and your partner can discuss this with your midwife team at your antenatal classes, where you can be advised by a midwife who is already aware of your own physical condition, of the latest safe practice in emergency delivery.
If you do go into labour en route to the hospital or at home when you are not expecting a home birth, call 999 immediately. You will be sent help by ambulance as quickly as possible, and your partner can be talked through any necessary support and action needed before professional aide arrives.

Most importantly, please do try not to worry about this happening, as it really does not happen very often and your fear may make you feel less confident and empowered at the thought of what is most likely going to be a happy, healthy and exhilarating (if exhausting!) birth.