Have you tried faxing the number,and asking them a question,ask them for a fax reply,and see if their reply gives up the fax number.

Flowers Direct here give out geographical numbers for those calling from overseas - specifically on their 'Contact Us' page here.

They have a Sales geographical of 01524 520800, and a Help geographical line of 01524 520836.

You could try ringing numbers ranging from 01524 520800 onwards (ie 01524 5208xx) but ringing out of hours from a phone that has inclusive minutes until you come across the fax machine number.  I know it's not 801 (01524 520 801) as I rung and spoke with someone. Sometimes the fax number is generally around the same as sales.

Alternatively, they know that outside the UK it is not always possible to ring numbers beginning with 08x so therefore you could think of an excuse to ring them that requires their fax number and say you have tried the 0871 but it isn't recognised do you have a geographical number for it beginning 01524 520 8xx.

Update:

A search of 192.com reveals a geographical fax number of 01524 520 826.  It is a fax number as I've just rung it.

I would recommend ringing them on their freephone number couple of minutes after you have faxed it as they may have more than one fax number or something.

Your wife can claim she had problems faxing and so you are just checking up to see if it went through all right.

They more than likely can't tell which number was dialled.

Looking on their website they have a different 0871 fax number than the one you posted so they may operate 2 or more faxes but it is possible though that both your 0871 fax number and the 0871 fax number listed on their website go to the same fax geographical fax number but this is unlikely as it would be a waste of an 0871 number.