Re: Alice Purser from UK
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It has been a while since your post so you may have the answers by now.
The 1901 census of England and Wales is now online at www.census.pro.gov.uk
I found a family Constance aged 30 Alice aged 7 and William aged 2 which fits best with the details in your post. They are living in Bedfordshire in a place called Pavenham Entire.
freebmd.rootsweb.com , which is a partial (but they are adding to it) online database of birth, marriage and death indexes, shows some Alices including one born Petworth in 1898.