This article originates from a 15 or 20 year old note in A-Antics Tech Tips that turned out to be wrong. It suggests using a radiator hose from an early 1960's Ford Falcon for the MGA, but that one turned out to be 3 inches too long. For many years the correct hose for the MGA has been available for a resonable price through the common British car parts suppliers, so this has been a non-issue, until now. For at least a couple years through 2005 and 2006 some after market hoses have been poor quality. Most of this time a better OEM type hose has been available, so we could have a choice. But recently the OEM type has disappeared from the market, and quality of the replacement type hose has changed to much worse than in the past. So it became time to resurect the search for a reasonable off the shelf replacement radiator hose for the MGA (and MGB).

The hose should be 1-1/8" ID x 6-3/4" Long
I have no idea who might make a flex hose with 1-1/8" bore, but there are lots of them available in 1-1/4" bore. Once I get the dimensions right (within reason) this is a very common hose both as original equipment as as a replacement for a lot of OEM applications.

I finally find one under a Dayco part number:
www.daycoproducts.com
    Dayco   81011 = 1-1/4 x 7-3/8
That is 1/8" oversize, but would easily pull down tight with a worm drive hose clamp. It is over length by just 3/8" at each end, so it might even work without trimming.

The rest was easy after finding a cross reference functions on the Dayco web site, and also NAPA cross reference.
The NAPA hose is 7-1/2 inches long, but for many of the cross reference numbers it says to "cut to length", so many of the other hoses noted will be a little shorter.

Some cross reference part numbers are:

AC Delco   31608 Atlas (Canada)   A507 Autopar   RH13 Autozone   C6402 Carlisle   507 CarQuest   25249 Dayco   1107 Dayco   81011 or DY81011 Durkee-Atwood   507 Ford   A9AZ-8260-A Gates  25249 Gates   26402 Gates   VF2 Goodyear   1107 Goodyear   52007 Hyundai   2350-15-185 John Deere   R54534 MG   AHH5143 (original no. for 1-1/8 x 6-5/8 hose, cross references from NAPA FF181, which is 1-1/4 x 7-1/2)

Mighty   1107 Mobile   5M7 Mopar   BH601 Motocraft   KA074 NAPA   FF181 NAPA   FM01 (discontinued, see FF181) Pep Boys   (Dayco 81011) Shell   1002 Sonoco   549 Texaco   102 Ultralast   C6402 Unical   1107 Uniroyal   5007 Uniroyal   5008 Western Auto   77-8300-4

The Dayco part DY81011 is spec'd to fit a long list of cars. See here:
http://www.racepages.com/products/?N=0&uts=true&Ntt=DY81011
Some of the newer ones are:
2002 – 2005 Lexus IS300
2002 – 2005 Mini Cooper - - - TA-DA!!! - That's current.
1993 – 2001 Nissan Altima
1999 – 2004 Rover Discovery

So now you can get your MGA radiator hose at a local auto parts store, a local car dealer, a number of service stations, or maybe even a tractor dealer.

Addendum July 2013:
On 7/13/2013, Matt Giesbrecht wrote:
"Goodyear now sells a flexible 1 1/8" ID radiator hose in varying lengths. - id=10520

The first Goodyear part number is 52109 1-1/8" x 9". There is a straight section at each end, so you can easily cut it down to get from 9 inches to 6-3/4" long.

Available from: www.rockauto.com

Addendum, 2/17/2016:
Here's a tip from Russell Goebel in Australia. There is a correct size good quality hose, 1-1/8-in (28mm) ID x 6-3/4-in long. The supplier is an Australian company, Mackay Consolidated Rubber Technology, an OEM supplier since 1932.