I was born in the U.S.  My mother, now in here late 70's, was born in
Great Britain and came to the U.S. shortly after WW2.

A few years after I was born, my mother became a naturalized U.S.
citizen, but has never formally renounced her UK citizenship.

Do I have any chance of becoming a UK citizen automatically on the
basis of my mother's UK citizenship at the time of my birth (or any
other basis for that matter)? Could I retain US citizenship too?

Hi wilmont,

1) Do I have any chance of becoming a UK citizen automatically on the
basis of my mother's UK citizenship at the time of my birth (or any
other basis for that matter)?

Yes!

I've tried to sort things out for you enough to help you make an
informed enquiry with the proper authorities. Everything always comes
down to personal circumstances that cannot be posted on such a public
forum as this and we can only guide you in the right direction.
Following is Britain's Immigration and Nationality website - there you
can view specific laws which may affect you and also read pamphlets
which may apply to your situation.

Immigration and Nationality website: Applying for British Nationality:
http://www.ind.homeoffice.gov.uk/default.asp

That said, after reading through the above website, I believe the
section of the law that applies to you is CHAPTER 2 SECTION 5.6,
"Automatic Acquisition".
(I've assumed you were born before 1983)

NATIONALITY INSTRUCTIONS
AUTOMATIC ACQUISITION ON 1 JANUARY 1983
EVIDENCE REQUIRED
2.5.6 A person born outside the United Kingdom or the Falkland Islands
before 1 January 1983 may be regarded as a British citizen on
production of:
# the relevant documents related to the person's, his or her parents',
grandparents', spouse's birth, adoption, marriage, death, registration
or naturalisation
http://www.ind.homeoffice.gov.uk/default.asp?PageId=1788

The next step is to contact the British Consulate nearest to you and
they will guide you the rest of the way.
British Missions and Consular Districts in the U.S.
http://www.usembassy.org.uk/cons_web/visa/us/missions.htm

2) Could I retain US citizenship too?

Yes!

"Unless you denounce your U.S. citizenship..you will keep it while
having dual citizenship U.S. and U.K."
http://www.americanexpats.co.uk/dual.htm


Additional Links:

Acquisition of British Citizenship:
British Citizenship can be acquired in the following ways:
1. By lex solis: By birth in the United Kingdom (excluding family
members of foreign diplomats or counsular staff)
2. By lex sanguinis (by descent): Children of a mother with British
citizenship, or legitimate children of a father with British
citizenship (provided the parent did not also acquire their
citizenship by descent).
3. By naturalisation
4. By registration 

Jus sanguinis (Redirected from Lex sanguinis)
"Jus sanguinis (latin for "right of blood") is a right by which
nationality or citizenship can be recognised to any individual born to
a parent who is a national or citizen of that state."
http://en.wikipedia.org/wiki/Lex_sanguinis

I hope this helps. If you have any questions, please post a
clarification request before rating my answer.

Thank you - and good luck,
hummer

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etc.

I beg to disagree with the answer. The reference above to automatic
aquisition only applies to people born in the UK or colonies, or
people born outside the UK who were already UK registered prior to
1983.

As your mother was born in the UK, you have the right of abode in the
UK, but not automatic citizenship. If you choose to move to the UK,
and live there continuously for 5 years (at least 9 months out of each
year), you will then be entitled to naturalisation after 5 years.

I'm going down this route myself. I'm Australian, have lived in the UK
for the past 4 years, and next year will be entitled to UK
naturisation (citzenship), and will be entitled to a UK passport then.

Thank you, eppy-ga, for your clarification.

Wilmont, eppy's note underlines the importance of calling the British
Consulate nearest to you to get first-hand, up-to-date information
tailored to your personal circumstances. If you were born between Feb
7 1961 and Jan 1 1983, I think the following pamphlet applies to you.
It includes a Guide on how to apply and also the registration form.

BN13: BN13: British citizenship - Adult children of British mothers:
Information about registration as a British citizen by certain people
born before 1983 to British mothers:
" You will be entitled to registration if:
    * you were born after 7 February 1961 but before 1 January 1983;
and
    * you were born to a mother who was a citizen of the United
Kingdom and Colonies at the time and you would have been a citizen of
the United Kingdom and Colonies by descent if it had been possible for
women to pass on citizenship of the United Kingdom and Colonies to
their children in the same way as men could; and
    * had you been a citizen of the United Kingdom and Colonies, you
would have had the right of abode in the United Kingdom and would have
become a British citizen on 1 January 1983
http://www.ind.homeoffice.gov.uk/default.asp?PageId=3854

Fees for registration:
http://www.ind.homeoffice.gov.uk/default.asp?PageId=1171

You'll find a list of pamphlets here:
http://www.ind.homeoffice.gov.uk/default.asp?PageId=38

This pamplet refers to what eppy-ga is talking about:
BN2: General Information about British Overseas citizenship
"9.  If you are a British Overseas citizen, you are entitled, on
applying, to be registered as a British citizen after you have lived
in the United Kingdom for five years (see Note F). You may be absent
from the United Kingdom for up to 450 days during this period without
losing your entitlement to be registered, but you can only be absent
from the United Kingdom for 90 days during the year immediately before
you apply. The Home Secretary may accept longer periods of absence in
the special circumstances of a particular case. You will normally have
to be free of restrictions under the immigration laws throughout the
year before you apply."

Different regulations will come into play for an Australian acquiring
British citizenship and an American acquiring British citizenship by
descent.

Good luck with your enquiries (it's never too early to start using the
British spelling of words!) at the Consulate and thank you for the
nice rating.

Sincerely,
hummer