Now as BSI has changed accreditation mark to ANAB, they are telling us to accept the ANAB. Can any one guide me on the influence of ANAB compare to UKAS in international market?
Firstly, BSi is still accredited (and I doubt they will ever drop it) by UKAS. So, if indeed are compelling reasons for it, I am certain they would issue you an UKAS accredited certificate.
As others have pointed out, in terms of "market recognition", UKAS and ANAB have similar standings.
There could be cases, however, where, due to contractual requirements, your certificate needs to have a specific accreditation. If I am not mistaken, in the UK some suppliers to the Ministry of Defence were required to attain UKAS accredited certification, in the past. So, check your contracts, specially, the military ones (If you have any).