The National Archives at Kew have microfiche of the Land Army index cards: MAF421 is the record series. You will need to visit TNA in person as the microfiche has not been digitised.
The original index cards are now lodged at the Imperial War Museum, but you won't gain anything by requesting to view a photocopy of a card as they hold no more information than the microfiche. The originals are not available to view.
Unfortunately, only the index cards survive and not the full service records. The information on the cards includes: full name (as "surname, forenames" which is how you search the fiche), address at enlistment, age at enlistment and date of birth, occupation at enlistment, WLA number (which would be of use if only the full service records had survived), and some sketchy details of where (by county) and when the individual was transferred between counties, plus how and when their service ended.
It was useful for me to be able to confirm when my mother signed up and her occupation/age/address at the time, and also when she resigned (and why, which I had to discern from reading between the lines of a pencilled 'Medical' annotation on the card), but I learned very little about her actual service -- much less than from her own reminiscences.