For those who don't know, as one example, this is a small slice of Qatari law. You can judge for yourself how similar it is to 'not purely secular' Britain:
'The constitution declares Islam to be the state religion and states sharia shall be “a main source” of legislation. According to the constitution, the Emir must be Muslim...The Emir exercises full executive power.'
'Conversion to another religion from Islam is defined by the law as apostasy and is illegal.'
'The law provides for a prison sentence of up to seven years for offending or misinterpreting the Quran, “offending” Islam or its rites or beliefs, insulting any of the prophets, or defaming, desecrating, or committing blasphemy against Islam, Christianity, or Judaism. '
'To obtain an official presence in the country, expatriate non-Muslim religious groups must register with the MFA.'
'According to the law, unregistered religious groups (i.e., those not registered or under the patronage of one of the registered groups) that engage in worship activities are illegal, and members of those groups are subject to deportation.
The law restricts public worship for non-Islamic faiths. It prohibits non-Muslim religious groups from displaying religious symbols, which includes banning Christian congregations from advertising religious services or placing crosses outdoors where they are visible to the public. The law criminalizes proselytizing on behalf of an organization, society, or foundation of any religion other than Islam and provides for punishment of up to 10 years in prison. Proselytizing on one’s own accord for any religion other than Islam may result in a sentence of up to seven years’ imprisonment. The law calls for two years’ imprisonment and a fine of 10,000 riyals ($2,700) for possession of written or recorded materials or items that support or promote missionary activity.
Public bookstores are not allowed to sell Bibles.
The only religions registered to have their own places of worship are Islam and Christianity.
A non-Muslim woman is not required by law to convert to Islam when marrying a Muslim; however, the law considers offspring of such a marriage to be Muslim. The law dictates that a non-Muslim man marrying a Muslim woman must convert to Islam.
Islamic instruction is compulsory for Muslim and non-Muslim students attending state-sponsored schools. Non-Muslims may provide private religious instruction for their children at home or in their faith services. All children may attend secular and coeducational private schools. The Ministry of Education requires that these schools must offer Islamic instruction, from preschool onwards, although students can opt-out of such instruction; non-Islamic formal religious education is prohibited.
A non-Muslim wife does not have the automatic right to inherit from her Muslim husband. She receives an inheritance only if her husband wills her a portion of his estate, and even then, she is eligible to receive only one-third of the total estate.
Qatar - United States Department of State