Just an update.............having seen Adam's recommendation for Xendpay, I decided to research and then give them a go.
I have now done two transfers to my daughter from the U.K., and the recent one arrived the following day.
More than happy, because unlike "World First" and many other companies, they do not have a minimum sum.
This is good for me, as with my daughter about to embark on University life, I am sure their will be many "incidentals" I suddenly have to send !!!!
The rate is very competitive, and the fee ( if you decide to pay the suggested amount) is 1% of transfer.
They have an I Phone App which I have used, and it works fine, but the only slight quibble I would have is that notification of funds being in recipient banks seems to be about 24 hours late. However I got my daughter to go on line with Bangkok Bank, and she can now let me know as soon as money is in.
The companies mantle of free transfers is not quite correct now however, as recently they have put in a clause that states that after transferring £2000 or the equivalent within one year, fees are applied, and I feel more comfortable with paying the 1 % transfer fee, as I am sure that will get prioritised over the free-bee merchants.
Anyway.... thought I would pass on my experience, and thank all in this thread for the valuable information regarding transfers.