According to the Encyclopedia Britannica the 1829 Emancipation Act left these protections of the Protestant religion of the Church of England in place:In 1829 this carefully restricted freedom again to practise the proscribed religion was extended by the statute commonly known as the Catholic Emancipation Act (io Geo. IV., c. 7). It further disestablished oaths and declarations against Transubstantiation, the invocation of saints and the sacrifice of the mass, by making such oaths and declarations no longer a qualification for member ship of parliament or the holding of any office, franchise or civil right, except offices in or connected with the Established churches, or in any educational institution in regard to which such oaths obtained. But a new oath, against any attempt to subvert the Protestant religion, was imposed upon Members of Parliament, naval, military and municipal officers and electors. Priests were forbidden to sit in the House of Commons, but all civil and mili tary offices were thrown open to Catholics, except the regency of the kingdom, the lord chancellorship, the lord-lieutenancy of Ire land and the high commissionership of the Church of Scotland.
Also they could not present to livings in the Church of England.
Many other restrictions upon religious liberty were maintained. Judicial and municipal officers were forbidden to attend in their insignia any public worship, except in a building of the Established Church; priests and monks were prohibited from conducting ceremonies or wearing habits save in their churches or private houses. Jesuits and all other male persons under religious vows already in the country were to register themselves—they did so for many years—and the entry into the country of those not already there was forbidden, with the exception of those of them who, being natural born British subjects, had left the country temporarily, and of others who might get a licence from a Protestant secretary of State to come into the country for a period not exceeding six months. To admit a person into a religious order was made a misdemeanour; the admitted person was to be banished for life, and transported for life if he had not gone within three months after the sentence of banishment. An attempt (apparently the only attempt) to enforce this law against religious orders was made as late as 1902, but the magistrate refused a summons and was upheld by the High Court : R. v. Kennedy; 86 Law Times Rep. 753. In 1898 parliament had declined to pass a bill for repealing the law, but it has now been repealed by the Roman Catholic Relief Act, 1926.
The author of the article in the Encyclopedia Britannica believes that Catholics are completely free to practice their religion in England as long as they don't interfere with the affairs of the Church of England, but he does offer a caveat to his stated confidence: