I'm looking into my family history and I'm trying to find the correct
spelling of my ancestors name. The spelling I have now is "Sicovsky" but
I don't think this is correct. I have also seen "Sekovsky", and in
both cases the y could be replaced with an i. The name comes from Riga
in Latvia at
about the turn of the 19th century. As far as I'm aware it's
pronounced shh - kov - ski

This is a tough one if you don't know the spelling.

By 'turn of the 19th century' do you mean 1799-1801-ish or 1899-1901-ish?

And presumably your ancestor went to America?

Do you consider your family to be of Latvian or Russian origin? 
If of Polish origin it would probably be Sikowski.

They left Latvia and went to the UK in the 1899-1901 ish turn of the
century, but actually could have been between 1860 - 1910.
I have done some internet research myself but came up with nothing. I
thought I would ask you guys before I searched out some Latvians..

I know for sure the family came from Riga, but wether they are Russian
by way of Latvia I don't know. Based on what I know I would consider
them to be from Latvia.

If they were in the UK in 1901 then they maybe on the 1901 census
which is accessible here:

http://www.1901census.nationalarchives.gov.uk/

It is helpful in these cases to do a G**gle search and then see how
many results come up for each as a way to measure which form is more
common:

Sicovsky: 1 result
://www.google.com/search?lr=&ie=UTF-8&oe=UTF-8&q=Sicovsky

Sekovsky: 18 results
://www.google.com/search?lr=&ie=UTF-8&oe=UTF-8&q=Sekovsky

Sekovski: 217 results
://www.google.com/search?num=50&hl=en&newwindow=1&safe=off&q=Sekovski&spell=1

So I vote for "Sekovski". Does Lithuanian use the Roman Alphabet or
Cyrillic cahracters?

Uh.. Latvian. Does _Latvian_ use the Roman Alphabet or Cyrillic cahracters?

Sample text in Latvian;

Visi cilv?ki piedzimst br?vi un vienl?dz?gi sav? pa?cie?? un ties?b?s.
Vi?i ir apvelt?ti ar sapr?tu un sirdsapzi?u, un vi?iem j?izturas citam
pret citu br?l?bas gar?.

http://www.omniglot.com/writing/latvian.htm

Also note this was introduced in the mid-1930's:

Latvian (Latvie?u)

Latvian is a Baltic language related to Lithuanian and Old Prussian
with about 1.4 million speakers in Latvia. There are also Latvian
speakers in the USA, Russia, Australia, Canada, Germany, the UK,
Sweden, Lithuania, Ukraine, Estonia, Brazil and Belarus.

The first publication to be printed in Latvian was a catechism which
appeared in 1585. The first Latvian dictionary, Lettus, was compiled
by Georg Mancelius in 1638. The German monks who wrote these texts
used a version of the the Fractur alphabet adapted from German which
was ill suited to the Latvian language. This alphabet was used until
the mid 1930s, when it was replaced with a modified version of the
Latin alphabet devised by Dr. J. Endzelins and K. Mühlenbach.

Same link.

According to "eleventh edition of the Encyclopedia Britannica, first
published in 1911"
http://60.1911encyclopedia.org/

Riga "now ranks seventh in the empire in order of population; 47% of
the inhabitants are Germans, 25% Russians and 23% Letts, with a small
admixture of Esthonians, Jews, &c"
http://30.1911encyclopedia.org/R/RI/RIGA.htm

Did your ancestors actually live in Riga? Or was Riga just their port of departure?

British "Census Records & Images" are available at
http://www.ancestry.co.uk/ (subscription required)

Do you know the first names of your ancestors coming from Riga?
Knowing their first names would help.

You could try to find your ancestors in the "All Latvia Database" ("a
work in progress and new entries are being added regularly")
http://www.jewishgen.org/databases/Latvia/

including

"Riga Tax Administration List"
http://www.jewishgen.org/databases/Latvia/RigaTax.htm

"The All Russia 1897 Census - Riga, Rezekne and Krustpils"
http://www.jewishgen.org/databases/Latvia/AllRussia.htm

"Riga Passport and Travel Documents Registration List 1900"
http://www.jewishgen.org/databases/Latvia/Passport.htm

A friend of mine who knows Latvia & some Latvians reports ...

All the Latvians I know have names ended in "s" -Jansons. Valdemars,
Nikolajs etc. His ancestors must have been immigrants!

I suppose that family names ending with -sky or -ski are Slavonic,
i.e. not Latvian.

More on "Naming of Latvians":
http://www.roots-saknes.lv/Names/Naming.htm

I tried to look the name up in the Latvian Phone Database, and I found
no "Sicovsky" or "Sekovsky" in it. The closest match that I have been
able to find was "Seikovsky" or "Seicovsky". This database includes
more than a third of Latvia's inhabitants - those who have phones.
There were other family names there, which differed from yours by one
letter, like "Siskovsky" or "Siscovsky".
The name is almost definitely of Polish origin, however, it does not
necessarily mean that your ancestors are Polish. I am Latvian myself,
however, my family name is German (from my great-great-grandfather,
who is the only German ancestor I have had, the rest are mostly
Latvian and I even have one Polish ancestor). There are many Latvians
in Latvia with Polish family names.
If there is anything else I can do to help with your search, let me know.

According to the 1901 census
http://www.ancestry.co.uk/

Marks and his wife Rine Sokoffsky were born in Russia, as was there
eldest son David. In 1901 they were living in London together with
their younger children Solomon and Rose both born in England.

Another possibility would be Sachofski:

According to the 1901 census
http://www.ancestry.co.uk/

Jacob and his wife Fanny Sachofski were born in Russia, as were three
of their children. In 1901 they were living in London. Four children
were born in England.

It might be easier - and more rewarding - to find the Tsar's jewels.

Over to you Freddy.

There are no Sokkofskys currently in Latvia who have a phone, however,
there are three Sachofskis, two of them in Riga - Stepan Sachofski and
Anna Sachofski.