Cancer

You cannot give blood if you have had cancer, even if the cancer has been treated and you are well at present

There are exceptions:

Carcinoma in-situ and Rodent Ulcer (Basal Cell Carcinoma)

You can donate if you have been cured of a carcinoma in situ (CIS) and discharged from follow-up (even if the you received radiotherapy as part of the treatment). You can donate if you have been returned to routine screening following treatment for cervical CIS. 

If you had Cervical Carcinoma in-situ / Cervical Dysplasia and you have completed successful treatment , you can give blood if no further treatment is planned even if you go for regular cervical smears

If you had Rodent Ulcer (Basal cell carcinoma) and you have completed successful treatment, you can give blood if no further treatment is planned